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WARMUP
 Find the slope of the line passing through the points
(-5, 8), and (23, -10).
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2) Graph the equation 𝑦 = − 𝑥 + 4
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using a table.
HOMEWORK: WKST 4.4
Reminder: Experiment for the next test. Retakes will not be allowed.
Also, You must take it within 2 days of the actual date or you will receive a
zero.
Questions on the WKST:
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LEARNING TARGET 4.3:
SLOPE-INTERCEPT FORM
1) Graph a linear equation in
slope-intercept form.
2) Graph and interpret
equations in slope-intercept
form that model real-life
situations.
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QUESTION:
What is slope-intercept form?
BAM!
𝑦 = 𝑚𝑥 + 𝑏
What does m stand for?
𝑚 = 𝑠𝑙𝑜𝑝𝑒
What does b stand for?
𝑏 = 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠 (where the graph of the line crosses the yaxis).
WRITING AN EQUATION OF A LINE IS
EASY IF YOU HAVE THE SLOPE AND
INTERCEPT!
Problem: Write an equation of the line whose slope m is 4 and whose yintercept b is -3.
Solution:
𝑚 = 4, 𝑎𝑛𝑑 𝑏 = −3
So, we substitute 4 for m, and -3 in for b in the equation 𝑦 = 𝑚𝑥 + 𝑏
𝑦 = 4𝑥 + (−3)
Now we simplify it:
𝑦 = 4𝑥 − 3
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SOMETIMES THERE MAY BE A ZERO
SLOPE OR ZERO INTERCEPT.
If there isn’t an intercepts or slope, don’t worry! Just plug in zero for that
value.
Example: Write an equation of the line in slope-intercept form with the
slope equaling 4, and the y intercepts equaling zero.
𝑦 = 𝑚𝑥 + 𝑏
𝑦 = 4𝑥 + 0, 𝑠𝑜
𝑦 = 4𝑥.
What would this line look like on a graph?
Note: since 𝑚 = 4, we rise 4, run 1.
SOMETIMES THERE MAY BE A ZERO
SLOPE OR ZERO INTERCEPT.
Example: Write an equation of the line in slope-intercept form with the
slope equaling 0, and the y intercepts equaling 3.
What would this look like?
𝑦 = 0𝑥 + 3
𝑦 = 3
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WRITING THE EQUATION FROM A
GRAPH WITH POINTS.
Example 2: Writing an Equation of a Line from a Graph can be tricky.
1) where does the graph cross the y axis?
That is your b value!!!
2) make sure that you identify two points that you can use to find the
slope.
NOTE: Sometimes you can find the slope from a graph by using 𝑚 =
Otherwise, put those points correctly into 𝑚 =
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
𝑦2 −𝑦1
𝑥2 −𝑥1
3) The solution is what m equals.
4) substitute both m and b into 𝑦 = 𝑚𝑥 + 𝑏, and you have done it!
WRITE AN EQUATION OF THE LINE
SHOWN IN THE GRAPH.
Example 2:
1) Where does the line intersect the y-axis?
𝑏 = −2. 𝑎𝑡 (0, −2)
2) Use two points to find the slope.
−4,0 𝑎𝑛𝑑 0, −2 (its ok to use the y-int).
3) plug it into 𝑚 =
𝑚=
−2−0
0−(−4)
2
4
𝑦2 −𝑦1
.
𝑥2 −𝑥1
=− =−
Or
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
1
2
Plug into 𝑦 = 𝑚𝑥 + 𝑏.
1
𝑦 = − 𝑥 + −2
2
1
𝑦 =− 𝑥−2
2
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YOU TRY! WRITE THE EQUATION OF
THE LINE
A FEW MORE TO PRACTICE ON.
 Find the equation of the line.
A.
B.
C.
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EQUATIONS OF HORIZONTAL AND
VERTICAL LINES.
In the coordinate plane, the graph of y = b is a
horizontal line.
In the coordinate plane,
the graph of x = a is a vertical line.
GRAPHING A LINE IN SLOPE
INTERCEPT FORM.
Make sure to put it into slope-intercept form first.
When graphing a line in slope-intercepts form 𝑦 = 𝑚𝑥 + 𝑏:
The y-intercepts, b is our starting point, and the slope m, is
𝑟𝑖𝑠𝑒
our directions. 𝑟𝑢𝑛
If m is a whole number, its simply whole number over 1.
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𝑖𝑓 𝑚 = 4, then 𝑚 = 1
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GRAPHING AN EQUATION IN SLOPE
INTERCEPT FORM: EXAMPLE 2:
𝟏
𝟑
Graph 𝒚 = 𝒙 − 𝟐 Clearly mark at least 2 points on the line.
Find the slope and y-intercept.
1
𝑚 =
b = –2
3
Graph y-intercept.
Use the slope to find
two more points.
Draw the line.
EXAMPLE 3: GRAPH AN EQUATION
IN SLOPE-INTERCEPT FORM
Graph the equation y = 2x - 3.
1. Find the slope, 2 , and the y-intercept, -3 .
2. Plot the point (0, b) when b is -3 .
3. Use the slope to locate a second point on the line.
𝑅𝑖𝑠𝑒 2
=
𝑅𝑢𝑛 1
Draw the line.
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OYO: GRAPH THE EQUATION IN SLOPEINTERCEPT FORM.
EXAMPLE 2
Graph each linear equation. Clearly mark at least thee
points on each line.
𝑦 = 6 – 2𝑥
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𝑦 =– 𝑥 + 1
2
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BREAKING EVEN
A break-even analysis will determine the quantity of a product
that must be sold before the seller begins to make a profit.
The analysis takes into consideration variable costs and fixed
costs.
Variable costs change with the quantity of product produced
while fixed costs remain constant. This is sometimes called
overhead costs.
Examples of fixed costs are rent, insurance, administrative
salaries, and equipment. Some variable costs are production
worker’s wages, material expense, and utilities expense.
REAL WORLD PROBLEMS: BREAK EVEN
A store can purchase T-shirts for $5 each. It has fixed costs of $500.
Each T-shirt is sold for $10.
1. Write a linear equation for both cost and revenue.
2. Graph both the cost line and the revenue line.
3. Determine the break-even point.
4. If the store wants to make a profit of
$2,000, how many T-shirts must it sell?
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YOU TRY
A hotdog stand can purchase hotdogs for $0.35 each and buns for $0.15
each. It has fixed costs of $50. Each hotdog is sold for $2.
1. Write a linear equation for both cost and revenue.
2. Graph both the cost and revenue lines.
3. Determine the break-even point.
HOMEWORK
P.244-245
13-45 odd
66-68all
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