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Algebra 1 Bell Ringer
Find the slope of the line that passes
through the points.
1. (2, –1), (4, 0)
2. (–1, –3), (1, 5)
3. A landscape architect charges $75 for a consulting
fee and $30 per hour. Write an equation that shows
the cost C as a function of time t (in hours).
Chapter 5
Writing Linear Equations
Prerequisite Skills
Page 280: 1-9
5-1
Objective: Write Linear
Equations in Slope-Intercept
Form
Review of Lingo
• Y-intercept
• Slope
• Slope-Intercept Form
Slope Intercept Form
• y = mx + b
• m = slope
• b = y-intercept
Use Slope and Y-intercept to Write
an Equation
• Just plug it in!
• Write an equation of the line with a slope
of 3 and a y-intercept of 5.
• What would the graph look like?
EXAMPLE 1
Use slope and y-intercept to write an equation
Write an equation of the line with a slope of –2 and
a y-intercept of 5.
y = mx + b
Write slope-intercept form.
y = –2x + 5
Substitute –2 for m and 5 for b.
Question
• What if you had to write an equation just
by looking at the graph? How would you
do it?
EXAMPLE 2
Standardized Test Practice
Which equation represents the line shown?
The slope of the line is rise = –2 = – 2 .
run
5
5
The line crosses the y-axis at (0, 3). So, the
y-intercept is 3.
Write slope-intercept form.
y = mx + b
y=– 2 x+3
5
Substitute – 2 for m and 3 for b.
5
GUIDED PRACTICE
for Examples 1 and 2
Write an equation of the line with the given slope
and y-intercept.
1.
Slope is 8; y-intercept is –7.
ANSWER
y = 8x – 7
GUIDED PRACTICE
for Examples 1 and 2
Write an equation of the line with the given slope
and y-intercept.
2. Slope is 3 ; y intercept is –3.
4
3x–3
ANSWER
y= 4
More Examples
• Page 286: 11, 12
Using Two Points
• If you know where the y-intercept is and
any other point on the line, then you can
write an equation of the line.
• How?
EXAMPLE 3
Write an equation of a line given two points
Write an equation of the line shown.
EXAMPLE 3
Write an equation of a line given two points
SOLUTION
STEP 1 Calculate the slope.
STEP 2
y –y
–1 – (–5)
4
m = x2 – x1 =
=
3–0
2
1
3
Write an equation of the line. The line crosses
the y-axis at (0, –5). So, the y-intercept is –5.
y = mx + b
Write slope-intercept form.
y= 4 x–5
3
Substitute 4 for m and 5 for b.
3
More Examples
• Guided Practice #3 on bottom of page 284
• Page 287: 23
Function Notation
• Review of Function Notation
Evaluate f(x) = 2x + 1 when x = 3
f(3) = 2(3) + 1
f(3) = 7
*This represents the point (3, 7)
Practice
• f(x) = 2x – 3 when x = 7, what point would
this be?
• f(x) = ½x – 7 when x = -6, what point
would this be?
Question
• If you only see f(0) = 5 what point is this
and why is it so valuable?
Example
• Write an equation for the linear function f
with the values f(0) = -2 and f(3) = -6
Example
• Write an equation for the linear function f
with values f(0) = 4 and f(9) = 10.
EXAMPLE 4
Write a linear function
Write an equation for the linear function f with the
values f(0) = 5 and f(4) = 17.
SOLUTION
STEP 1
Write f(0) = 5 as (0, 5) and f (4) = 17 as (4, 17).
STEP 2
Calculate the slope of the line that
passes through (0, 5) and (4, 17).
y2 – y1
m=
x2 – x1 =
17 – 5
4–0
12
= 4 =3
EXAMPLE 4
STEP 3
Write a linear function
Write an equation of the line. The line crosses
the y-axis at (0, 5). So, the y-intercept is 5.
y = mx + b
Write slope-intercept form.
y = 3x + 5
Substitute 3 for m and 5 for b.
ANSWER
The function is f(x) = 3x + 5.
GUIDED PRACTICE
3.
for Examples 3 and 4
Write an equation of the line shown.
ANSWER
y=– 1 x+1
2
GUIDED PRACTICE
4.
for Examples 3 and 4
Write an equation for the linear function f with the
given values.
f(0) = –2, f(8) = 4
ANSWER
y= 3 x–2
4
GUIDED PRACTICE
5.
for Examples 3 and 4
Write an equation for the linear function f with the
given values.
f(–3) = 6, f(0) = 5
ANSWER
y = – 13 x + 5
Real-World Situations
• Remember key words: per, for each, for
every…, etc., tells you to multiply. In this
section, this will represent your slope.
Example
• The YMCA charges an initial membership
fee of $45 and $60 per month to work out
in the gym.
Write an equation that gives the total cost of
being a member and working out every
month.
Find the amount you would spend if you worked
out every month for a year.
Look over Example 5
Homework
• 1, 2 – 36 ev, worksheet
bonus 44, 52