# Writing Equations in Point ```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 = &frac12;, the equation is y = -2x + &frac12;
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
2. m = -6 and b = &frac12;
3. m = 0 and b = 8
4. m = -2 and b = 0
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Writing Equations Using Slope-Intercept Form
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 = 3
1 = 3(2) + b
1=6+b
-5 = b
identify x, y and m
substitute x, y and m into y = mx + b
simplify 3 times 2
solve 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 = -&frac14;
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Writing Equations Using Slope-Intercept Form
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.
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) + b
substitute into y = mx + b
2=0+b
2=b
simplify
solve 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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