Writing Equations Using Slope-Intercept Form

Objective: As an alternate to point-slope form, the learner will use slope-intercept form to write the equation of a line.

Prerequisite skills: The learner should be familiar with graphing using slope-intercept form

Lesson Plan:

The slope-intercept form of an equation is not only useful in graphing lines, it helps us to write an equation of a line given some key information.

Recall that for y=mx+b, m is the slope and b is the y-intercept. If we know m and b, we can write the equation of a line by inserting these numbers into y=mx + b

For example:

  1. Given m= 3 and b = 5, the equation is y = 3x + 5
  2. Given m = -2 and b = ½, the equation is y = -2x + ½

Now you try. Write the equation of a line in slope-intercept form given the following. Simplify if possible.

  1. m = 7 and b = 4
  1. m = -6 and b = ½
  1. m = 0 and b = 8
  1. m = -2 and b = 0

What if we are given m and a point (x,y) but not b?Can we still write the equation of the line?

We can use Slope-intercept form, y = mx + b, to write the equation of a line because we’ve been given m, x and y. Just plug in and solve for b!

The steps to writing an equation using slope-intercept form are as follows.

  1. Identify x, y and m from information given
  2. Substitute in x, y and m into y = mx + b
  3. Solve for b
  4. Write the equation y = mx + b substituting in JUST m and b

Example: Write the equation in slope-intercept form given the slope and a point.

(2,1), m = 3

x = 2, y = 1, m = 3identify x, y and m

1 = 3(2) + bsubstitute x, y and m into y = mx + b

1 = 6 + bsimplify 3 times 2

-5 = bsolve for b by subtracting 6 from both sides

Now write the equation of the line by substituting in m and b into y = mx + b

y = 3x - 5

Let’s work these together. Write the equation in slope-intercept form given the slope and a point.

(1,3), m = -2(4,-2), m = -¼

Sometimes you are given two points on the line but no slope. We’ll still use the slope-intercept form, but first we have to find the slope ourselves.

Follow these steps:

  1. Find the slope using the 2 given points and the formula for slope
  2. Use one of the points and the slope to substitute into slope-intercept form
  3. Solve for b
  4. Write the equation y = mx + b substituting in JUST m and b

Here’s an example:

Given points (0,2) and (4,3) write the equation of a line in slope-intercept form.

Recall that slope, m =

m = =

You can use either point to substitute into y = mx + b. I will use (0,2).

x = 0, y = 2, m = identify x, y and m

2 = (0) + bsubstitute into y = mx + b

2 = 0 + bsimplify

2 = bsolve for b

Use this b and m to write your equation:

y =x + 2

Let’s work these together.

Given points (0,0) and (-1,-5) write the equation of a line in slope-intercept form.

Given points (2,2) and (4,-1) write the equation of a line in slope-intercept form.

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