How to find slope and y intercept on a graph

Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.

Example

Find the equation of the line

Choose two points that are on the line

Calculate the slope between the two points

$$m=\frac{y_{2}\, -y_{1}}{x_{2}\, -x_{1}}=\frac{\left (-1 \right )-3}{3-\left ( -3 \right )}=\frac{-4}{6}=\frac{-2}{3}$$

We can find the b-value, the y-intercept, by looking at the graph

b = 1

We've got a value for m and a value for b. This gives us the linear function

$$y=-\frac{2}{3}x+1$$

In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.

We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope

The#y#-intercept#b#can be found by reading the#y#-axis where the graph hits the y-axis, and the slope#m#can be found by finding any two distinct points#(x_1,y_1)#and#(x_2,y_2)#on the graph, and using the slope formula below.

Every straight line can be represented by an equation: y = mx + b. The coordinates of every point on the line will solve the equation if you substitute them in the equation for x and y.

The slope m of this line - its steepness, or slant - can be calculated like this:
                                            m = change in y-value
                                                   change in x-value

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.

The y-intercept of this line is the value of y at the point where the line crosses the y axis.

In this lesson, we learn how to graph our line using the y-intercept and the slope. First, we know that the y-intercept (b) is on the y-axis, so we graph that point. Next, we use the slope to find a second point in relation to that intercept. The following video will show you how this is done with two examples.

Video Source (05:37 mins) | Transcript

Steps for graphing an equation using the slope and y-intercept:

1. Find the y-intercept = b of the equation y = mx + b.
2. Plot the y-intercept. The point will be (0, b).
3. Find the slope=m of the equation y = mx + b.
4. Make a single step, using the rise and run from the slope. (Make sure you go up to the right if it’s positive and down to the right if it’s negative.)
5. Connect those two points with your line.

Additional Resources

• Khan Academy: Intro to Slope-intercept Form (08:59 mins, Transcript)
• Khan Academy: Graph from Slope-intercept Equations (03:01 mins, Transcript)
• Khan Academy: Slope-intercept Examples (03:45 mins, Transcript)

Practice Problems

1. Plot the line \({\text{y}}=-3{\text{x}}+2\) starting with the y-intercept and then using the slope.
2. Plot the line \({\text{y}}=\frac{1}{2}{\text{x}}-3\) starting with the y-intercept and then using the slope.
3. Plot the line \({\text{y}}=-\frac{3}{5}{\text{x}}+1\) starting with the y-intercept and then using the slope.
4. Plot the line \({\text{y}}=2{\text{x}}+3\) starting with the y-intercept and then using the slope.
5. Plot the line \({\text{y}}=-{\text{x}}-4\) starting with the y-intercept and then using the slope.
6. Plot the line \({\text{y}}=\frac{4}{5}{\text{x}}+4\) starting with the y-intercept and then using the slope.

Solutions

1. Note: The graph you create may look slightly different depending on the spacing you choose for your x and y-axis. The correct graph should still have the same direction of slope and the x and y-intercepts should be the same.
   
   
   (Written Solution)

   To graph this line we need to identify the slope and the y-intercept. The equation is written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept.

   Step 1: Find the slope and the y-intercept of the line:

   The equation of the line is

   \({\text{y}}={\color{red}-3}{\text{x}}{\color{Blue}+2}\)

   So the slope is \({\color{red}-3}\), and the y-intercept is 2.

   Step 2: Graph the y-intercept:

   

   This is a picture of a coordinate plane with the points \((0, -4)\) and \((1, -5)\) graphed on it. There is a line passing through both points.

   How do you find a y

   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.

   How do you find the slope in a graph?

   Finding Slope From a Graph.

   Select any two random points on the graph of the line (preferably with integer coordinates)..

   Label them as A and B (in any order)..

   Calculate the "rise" from A to B. While going vertically from A to B, if we have to go. ... .

   Calculate the "run" from A to B. ... .

   Now, use the formula: slope = rise/run..

   How do you find the slope and y

   The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.