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:
- Find the y-intercept = b of the equation y = mx + b.
- Plot the y-intercept. The point will be (0, b).
- Find the slope=m of the equation y = mx + b.
- 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.)
- 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
- Plot the line \({\text{y}}=-3{\text{x}}+2\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=\frac{1}{2}{\text{x}}-3\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=-\frac{3}{5}{\text{x}}+1\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=2{\text{x}}+3\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=-{\text{x}}-4\) starting with the y-intercept and then using the slope.
- Plot the line \({\text{y}}=\frac{4}{5}{\text{x}}+4\) starting with the y-intercept and then using the slope.
Solutions
- 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.