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Find the slope of the line in the graph. And just as a bit of a review, slope is just telling us how steep a line is. And the best way to view it, slope is equal to change in y over change in x. And for a line, this will always be constant. And sometimes you might see it written like this: you might see this triangle, that's a capital delta, that means change in, change in y over change in x. That's just a fancy way of saying change in y over change in x. So let's see what this change in y is for any change in x. So let's start at some point that seems pretty reasonable to read from this table right here, from this graph. So let's see, we're starting here-- let me do it in a more vibrant color-- so let's say we start at that point right there. And we want to go to another point that's pretty straightforward to read, so we can move to that point right there. We could literally pick any two points on this line. I'm just picking ones that are nice integer coordinates, so it's easy to read. So what is the change in y and what is the change in x? So first let's look at the change in x. So if we go from there to there, what is the change in x? My change in x is equal to what? Well, I can just count it out. I went 1 steps, 2 steps, 3 steps. My change in x is 3. And you could even see it from the x values. If I go from negative 3 to 0, I went up by 3. So my change in x is 3. So let me write this, change in x, delta x is equal to 3. And what's my change in y? Well, my change in y, I'm going from negative 3 up to negative 1, or you could just say 1, 2. So my change in y, is equal to positive 2. So let me write that down. Change in y is equal to 2. So what is my change in y for a change in x? Well, when my change in x was 3, my change in y is 2. So this is my slope. And one thing I want to do, I want to show you that I could have really picked any two points here. Let's say I didn't pick-- let me clear this out-- let's say I didn't pick those two points, let me pick some other points, and I'll even go in a different direction. I want to show you that you're going to get the same answer. Let's say I've used this as my starting point, and I want to go all the way over there. Well, let's think about the change in y first. So the change in y, I'm going down by how many units? 1, 2, 3, 4 units, so my change in y, in this example, is negative 4. I went from 1 to negative 3, that's negative 4. That's my change in y. Change in y is equal to negative 4. Now what is my change in x? Well I'm going from this point, or from this x value, all the way-- let me do that in a different color-- all the way back like this. So I'm going to the left, so it's going to be a negative change in x, and I went 1, 2, 3, 4, 5, 6 units back. So my change in x is equal to negative 6. And you can even see I started it at x is equal to 3, and I went all the way to x is equal to negative 3. That's a change of negative 6. I went 6 to the left, or a change of negative 6. So what is my change in y over change in x? My change in y over change in x is equal to negative 4 over negative 6. The negatives cancel out and what's 4 over 6? Well, that's just 2 over 3. So it's the same value, you just have to be consistent. If this is my start point, I went down 4, and then I went back 6. Negative 4 over negative 6. If I viewed this as my starting point, I could say that I went up 4, so it would be a change in y would be 4, and then my change in x would be 6. And either way, once again, change in y over change in x is going to be 4 over 6, 2/3. So no matter which point you choose, as long as you kind of think about it in a consistent way, you're going to get the same value for slope.

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Finding slope from graph | Algebra (video) | Khan Academy

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The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y=f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the x-intercept and the y-intercept. An intercept of a function is a point where the graph of the function cuts the axis. Let us understand the meaning of y-intercept and the calculation of y-intercept using the y-intercept formula with a few examples.

What is Y-Intercept?

The y-intercept of a graph is (are) the point(s) where the graph intersects the y-axis. We know that the x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.

Here is an example of a y-intercept. Consider the line y = x+ 3. This graph meets the y-axis at the point (0,3). Thus (0,3) is the y-intercept of the line y = x+ 3.

Y-Intercept of a Straight Line

When two planes intersect we get a straight line. A straight line can be horizontal or vertical or slanting. The y intercept of a horizontal line is (0, a) and the y intercept of a vertical line does not exist. Let us learn to find the y intercept of a straight line represented in different forms.

Y-Intercept in The General Form

The equation of a straight line in general form is ax+by+c=0. For y-intercept, we substitute x=0 and solve it for y.

a(0)+ by + c =0

by + c =0

y = - c/b

Thus, the y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b

y-Intercept in The Slope-Intercept Form

The equation of the line in the slope-intercept form is, y=mx+b. By the definition of the slope-intercept form itself, b is the y-intercept of the line. You try by substituting x=0 in y=mx+b and see whether you get b as the y-intercept. Thus, the y-intercept of the equation of a line in the slope-intercept form is (0, b) or b.

y-Intercept in The Point-Slope Form

The equation of the line in the point-slope form is, y-y\(_1\)=m x-x\(_1\). For y-intercept, we substitute x=0 and solve it for y.

y-y\(_1\) = m (0-x\(_1\) )

y-y\(_1\)= - mx\(_1\)

y = y\(_1\) - mx\(_1\)

Thus, the y-intercept of the equation of a line in the point-slope form is: (0, y\(_1\) - mx\(_1\)) or y\(_1\) - mx\(_1\)

Y-Intercept Formula

The y-intercept of a function is a point where its graph would meet the y-axis. The x-coordinate of any point on the y-axis is 0 and we use this fact to derive the formula to find the y-intercept. i.e., the y-intercept of a function is of the form (0, y). Thus, the formula to find the y-intercept is:

Y Intercept Formula

To find the y-intercept of a function y = f(x),

we just substitute x = 0 in it.

solve for y.

represent the y-intercept as the point (0, y).

How To Find Y-Intercept?

We have derived the formulas to find the y-intercept of a line where the equation of the straight line is in different forms. In fact, we do not need to apply any of these formulas to find the y-intercept of a straight line. The y-intercept of the polynomial function of the form \(y=a_1x^n+a_2 x^{n-1}+...+a_n\) is just its constant term \(a_n\) (or) \((0, a_n)\).

We just substitute x=0 in the equation of the line and solve for y. Then the corresponding y intercept is y or (0, y).

The y-intercept of a function can be easily found by graphing it using the graphing calculator and locating the point where the graph cuts the y-axis. A function has only one y-intercept because otherwise, it fails the vertical line test. The y- intercept of the second equation of the table is shown in the graph below.

y-intercept of a Quadratic Function or a Parabola

The procedure for finding the y-intercept of a quadratic function ( parabola) is the same as that of a line (as discussed in the previous section). If a quadratic equation is given, substitute x = 0 and solve for y to get the y intercept.

Examples
Important Notes

We substitute x=0 and solve for y to find the y-intercept.

In the same way, we substitute y=0 and solve for x to find the x-intercept.

The lines parallel to the y-axis cannot have y-intercepts as they do not intersect the y-axis anywhere.

The y-intercept of a line is widely used as an initial point while graphing a line by plotting two points.

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Examples of Y Intercept
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FAQs on y Intercept

What is Y Intercept?

The y-intercept of a graph is (are) the point(s) where the graph intersects the y-axis.

What is the slope and y Intercept of y = 6?

Comparing y=6 with y=mx+b, we get, m = 0 and b=6

Here, m is the slope of the line.

Thus, the slope of y = 6 is 0. The y intercept is 6.

What is the y-intercept of y= 3x?

To find the y-intercept, substitute x=0

Then y=3(0)=0

So the y-intercept of y=3x is (0,0)

How do you find the y-intercept on the graphing calculator?

We use the button "y=" on the calculator to enter the function and then press on the "graph."Then the graph of the function is displayed on the screen.

Then press on the "zoom" button.

Then press on the "trace" button and enter 0

It will then show the value of y at which x is 0

What Is Y Intercept Formula?

The y-intercept formula is used to find the y-intercept of a function. i.e., it is used to find the point where the graph of the function cuts the x-axis. The formula to find y-intercept says that the y-intercept of a function y = f(x) can be found by substituting x = 0 in it.

How To Derive Y Intercept Formula?

According to the definition of y-intercept, the y-intercept of a graph is the point where it cuts (or) intersects the y-axis. We know that on the y-axis the x-coordinate is 0. Hence the formula to find the y-intercept of a function y = f(x) is just substituting x = 0 and solving for y.

What Are the Applications of Y Intercept Formula?

The y-intercept formula is used to find the y-intercept of a function. The y-intercept is mainly used in the process of graphing a function.

Find the y-intercept of the graph of y= x+(1/x)?

To find the y-intercept of the given graph, we substitute x=0. Then we get: y=0+ 1/0 = ∞

Hence the given graph has no y-intercept. It means the graph does not intersect the y-axis anywhere.

Find The y Intercept of The Graph represented by the equation x = y²+2 y-3.

To find the y-intercept, we substitute \(x=0\) in the given equation and solve for \(y\). Then,

y-intercepts are (0, -3) and (0, 1)

How To Use the Y Intercept Formula in Finding the Y Intercept From a Graph?

The y-intercept formula says that the y-intercept of a function y = f(x) is obtained by substituting x = 0 in it. Using this, the y-intercept of a graph is the point on the graph whose x-coordinate is 0. i.e., just look for the point where the graph intersects the y-axis and it is the y-intercept.

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Y Intercept - Meaning, Examples | Y Intercept Formula

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The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y=f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the x-intercept and the y-intercept.

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Slope problems are presented along with their detailed solutions.