Name: ___________________________ Per. _____EOC Ch3 B Linear Functions & Inequalities:
A1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a
point on the line, or two points on the line, and translate between forms of linear equations.
Study Notes: There are 3 forms of linear equations.
 y = a + bx, slope intercept form: a = starting value, b = slope
 y = y1 + b(x – x1), point slope form: b = slope and (x1, y1) is a point on the line.
 ax + by = c, standard form
Slope =
𝒚𝟐 −𝒚𝟏
𝒙𝟐 −𝒙𝟏
or the change in y divided by the change in x.
Strategy: Study all three forms to help you recognize the important features of a line. Some textbooks
use y = mx + b for slope intercept where m = slope and b = y-intercept. Given y = 3x + 5
The slope = 3 and the y-intercept would be 5 or (0, 5)
Examples
Practice
Example #1: Find an equation for a line with y1. Write the equation for the line with
intercept equal to -2 and slope equal to 3.
slope 7 and y-intercept 23.
A. 7x + 23y = 0
B. y = 23x + 7
C. x = 7y + 23
D. y = 7x + 23
A. y = -2x + 3
B. y = -2x – 3
C. y = 3x – 2
D y = 2x – 2
C is the only choice where the slope = 3. The y- 2. Write the equation for a line with
intercept for choice C is -2.
slope 5 and passes through the point
(2, 7).
Solution: C
__________________________________
A. y = 7 + 5(x – 2)
Example #2: Find an equation for a line with a slope B. y = 7 + 5(x + 2)
of -1 that goes through the point (-3, 2).
C. y = 2 + 5(x – 7)
D. y = 2 + 5(x + 7)
A. y = –x +1
B. y = -x – 1
3. Find the slope of the line that
C. y = 2x – 1
contains the points (3, 6) and (5, 14).
D. y = 3x – 2
Use point-slope form to write the equation.
b = -1, x1 = -3 and y1=2, substitute the values into
y = y1 + b(x – x1) equals y = 2 + -1(x - -3).
y = 2 -1(x + 3).
Simplify the negatives
y=2–x–3
Distributive Property
y = -1 – x.
Combine like terms
Solution: B
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Study Note:
y = 2x + 3 is the same equation as y = 3 + 2x
y = 8 – .5x is the same equation as y = -.5x + 8
4. Write the equation for a line that
passes through the points (8, -1) and
(-4, 5)
A. y = 5 - 2(x – 4)
B. y = 5 - 2(x + 4)
1
C. y = 5 - 2(x – 4)
1
D. y = 5 - 2 (x + 4)
Name: ___________________________ Per. _____EOC Ch3 B Linear Functions & Inequalities:
A1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a
point on the line, or two points on the line, and translate between forms of linear equations.
Study Notes: There are 3 forms of linear equations.
 y = a + bx, slope intercept form: a = starting value, b = slope. When graphing the
starting value is the y-intercept. Mark this point and then use the slope to graph the line.
 y = y1 + b(x – x1), point slope form: b = slope and (x1,y1) is a point on the line. When
graphing, plot the point, (x1,y1) then use the slope to graph the line
 ax + by = c, standard form. IN order to graph standard from change it into slopeintercept form.
Slope =
𝒚𝟐 −𝒚𝟏
𝒙𝟐 −𝒙𝟏
or the change in y is the rise and the change in x is the run..
Examples
Practice
1
2
1. Graph the line y = -2 + 3x
Example #1: Graph y = 1 - x
3



Plot the point (0,1).
Then graph rise 2
and back (left) 3 or
Graph down 2 and
right 3
__________________________________
Example #2: Graph the line y = 1 + 2(x + 2)



Plot the point (-2,1).
Then graph rise 2
and run 1 or
Graph down 2 and
left 1
__________________________________
Example #3: Graph the line 3x - 2y = 8

Solve for the equation
for y
subtract 3x -2y = -3x + 8
divide by -2
y = (3/2)x - 4

2. Graph the line y = 3 – (x – 1)
Then follow the steps in
example #1 to graph the
line
3. Graph the line 2x + 4y = -4