Download Writing Equations of Lines Review

Algebra 1
Writing Equations Review
Name ______________________________
Three Forms of Linear Equations
1) Slope-Intercept Form: _____________________________
2) Point-Slope Form: ________________________________
3) Standard Form: __________________________________
Writing an Equation Given a Slope and a Y-intercept
Steps to writing an equation given the SLOPE and the Y-INTERCEPT:
a) Write slope-intercept form.
b) Substitute in the slope (m) and the y-intercept (b).
c) If necessary, convert your equation from step 2 to the correct form asked in the
problem.
4) Write an equation of the line
in slope-intercept form.
𝑚 = −3 𝑏 = −5
5) Write an equation of the line
in standard form.
1
𝑚=2 𝑏=4
Writing an Equation Given a Point and the Slope
Steps to writing an equation given a POINT and the SLOPE:
a) Write down point-slope form.
b) Substitute in the slope (m) and the point (x1, y1).
c) If necessary, convert your equation from step 2 to the correct form asked in the
problem.
6) Write an equation of the line.
in slope-intercept form.
 2, 2 , m  5
7) Write an equation of the line
in standard form.
8,1, m  3
Writing an Equation Given 2 Points
Steps to writing the equation given TWO POINTS:
a) Find the slope.
b) Substitute the slope (m) and one point (x1, y1) into point-slope form.
c) If necessary, convert your equation from step 2 to the correct form asked in the
problem.
8) Write the equation of the line
in slope-intercept form.
(-5, 7) and (2, -7)
9) Write the equation of the line
in standard form.
(2, 0) and (-2, 6)
Writing Equations of Parallel and Perpendicular Lines
Parallel Lines:
10) The slope (m) of parallel lines are the __________________________
Perpendicular Lines:
11) The slope (m) of perpendicular lines are __________________________
Steps to writing the equation of parallel/perpendicular lines:
a)
Identify the slope of the original line in the problem.
b)
Find the slope of a line parallel/perpendicular to the original line.
c)
Substitute the slope (m) from part 2 and the point (x1, y1) into point-slope form.
d)
If necessary, convert your equation from step 3 to the correct form asked in the
problem.
12) Write the equation of a line that is parallel to the given line and passes through the given
point.
𝑥 + 5𝑦 = 10 (4, −3)
13) Write the equation of a line that is perpendicular to the given line and passes through the
given point.
1
y   x  1 (−3,5)
7
Writing Equations Vertical and Horizontal Lines
14) A horizontal line will be an equation in the form: _______________
Recall Slope (m) = ________________
15) A vertical line will be an equation in the form: _________________
Recall Slope (m) = ________________
Write the equation of the lines below. Also, identify their slopes.
16)
17)
equation: _____________________
equation: _____________________
m = ___________
m = ___________
Writing Equations from Graphs
Steps to Writing an equation from a GRAPH:
a) Identify the y-intercept (b) : Where does the line cross the y-axis?
b) Identify the Slope (m) : Use m =
rise
run
.
c) Substitute only (m) and (b) into slope-intercept form: y = mx + b.
Write an equation of the lines below.
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19)