Writing linear equations in slope intercept form answer key

The slope-intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y=mx+b. Other forms of linear equations are the standard form and the point-slope form.

Equations of lines have lots of different forms. One form you're going to see quite often is called the slope intercept form and it looks like this: y=mx+b, where m stands for the slope number and b stands for the y intercept.
So, when you're doing problems where you're asked to write the equation in slope intercept form, you only need two pieces of information. The first piece of information you need is the slope number and the second piece of information you need is the y intercept. Once you have those two pieces, those two numbers, you just plug them in there and you're on your way.

An equation in the slope-intercept form is written as

$$y=mx+b$$

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

$$m=-\frac{2}{3}$$

This gives us the equation

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

From this we can solve the equation for b

$$b=y+\frac{2}{3}x$$

And if we put in the values from our first point (-3, 3) we get

$$b=3+\frac{2}{3}\cdot \left ( -3 \right )=3+\left ( -2 \right )=1$$

If we put in this value for b in the equation we get

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

which is the same equation as we got when we read the y-intercept from the graph.

To summarize how to write a linear equation using the slope-interception form you

1. Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.
2. Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Once you've got both m and b you can just put them in the equation at their respective position.

Video lesson

Find the equation to the graph

How do you write a linear equation in slope

What is the slope