Notes
Writing Equations in
Slope-Intercept Form
We know that the equation of a line in slope-intercept form is 𝑦 = 𝑚𝑥 + 𝑏, where
m is ____________, and b is the ___________________.
*You will be given the following information: slope and y-intercept, slope and a
point, two points, and a graph, and will be asked to find the ________________.
**BIG IDEA: Regardless of the information in the problem, we are looking to
replace the ____ and ____ with numbers, and leave the ____ and ____ as
variables.
Writing Equations Given Slope and Y-Intercept
Example 1 : Find the equation of the line given a slope of 1 and a y-intercept of -4.
*In this example, 1 is ____ and -4 is _____. Rewrite 𝑦 = 𝑚𝑥 + 𝑏 with these new
numbers.
You try! - Find the equation of the line given:
4
1) slope = − , y-intercept = 5
5
2
3) y-intercept = -3, slope = ,
7
2) slope = -1, y-intercept = −
4) slope = 0, y-intercept = 0
1
3
Writing Equations Given Slope and a Point
A point on a given line is represented by the ordered pair ( ___ , ___ ), while ___
is slope.
In slope-intercept form, only ____ and ____ are replaced with numbers, so we
will use the given ____, ____, and ____ to find ____. ____ and ____ will remain
variables in our final answer.
Example 2: Find the equation of the line with slope of
1
2
that passes through
(−4, 4).
You try! - Find the equation of the line given the information provided.
5) slope = -1; (-3,-8)
1
7) slope = -5, ( , 4)
2
6) slope =
3
; (4, 0)
4
8) slope = undefined; (-1, -1)
*HINT: Think HOYVUX!
Writing Equations Given Two Points
Remember the formula for slope between (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ) is _____________
If the question gives you two points, start by using this formula to find ____.
Once you have slope, then you CHOOSE one of the two ordered pairs to use for
____ and ____. Solve for ____ and rewrite the equation.
**WARNING: The “x” and “y” you choose have to come from the SAME ORDERED
PAIR!!
Example 3 : Find the equation of the line that passes through (3, 5) and (−2, 20)
You try! - Find the equation of the line that passes through the given points.
9) (3,0); (−5,4)
10) (9,14); (−7, −2)
11) (0, −1); (4,2)
12) (8, 9); (−4,9)
*HINT: Think HOYVUX!
Writing Equations Given a Graph
Some of the time, you’ll be able to determine the equation of a graph by counting
slope and easily identifying the y-intercept. Of course, it isn’t always that easy…
Given a graph, pick ______ points on the graph, determine the (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 )
that go along with the points, and follow the steps from “Writing Equations Given
Two Points”
Example 4 : Write the equation of the line given the graph below:
You try! - Write the equation of each line graphed below:
13)
14)
*HINT: Think HOYVUX