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ALGEBRA 1
Lesson 5-2 Warm-Up
ALGEBRA 1
“Slope-Intercept Form” (5-2)
What is “slope-intercept form”
slope-intercept form: a linear equation (forms a line) which include the slope of the line and its y-intercept (where the line crosses the y-axis) – It is written as:
where m (the coefficient of the x term) is the slope and b is the y-intercept (where the line crosses the y-axis)
ALGEBRA 1
The slope is 2 and the y-intercept is –3.
What are the slope and y-intercept of y = 2x – 3?
mx + by =
2x – 3
Use the Slope-Intercept form.
y =
Slope-Intercept FormLESSON 5-2
Additional Examples
ALGEBRA 1
Write an equation of the line with slope and
y-intercept 4.
25
Use the slope-intercept form.y = mx + b
y = x + 425
25Substitute for m and 4 for b.
Slope-Intercept FormLESSON 5-2
Additional Examples
ALGEBRA 1
y = mx + b
Step 2 Write an equation in
slope–intercept form. The y-intercept is 1.
Write an equation for the line.
Step 1 Find the slope. Two points
on the line are (0, 1) and (3, –1).
–1 – 1 3 – 0
slope =
= – 23
23
y = – x + 1
Substitute – for m and 1 for b.
23
Slope-Intercept FormLESSON 5-2
Additional Examples
ALGEBRA 1
“Slope-Intercept Form” (5-2)
How can you determine if a point lies on the line of an equation?
Every point that lies on the graph of an equation must make the equation true. Therefore, to verify (check) whether a point lies on a line, substitute the x and y values of the equation for the x and y coordinates of the point. If the result is a true statement (both sides equal one another), the point is a solution for that equation (in other words, it is part of the graph of that equation).
Example:
ALGEBRA 1
Determine whether (1, 2) lies on the graph of
y = 3x – 1.
y = 3x – 1
2 3(1) – 1 Substitute 1 for x and 2 for y.
2 3 – 1 Multiply.
2 = 2 Subtract.
(1, 2) is a solution.
Slope-Intercept FormLESSON 5-2
Additional Examples
ALGEBRA 1
“Slope-Intercept Form” (5-2)
How do you graph an equation.
There are two ways to graph an equation.
Method 1: Slope-Intercept Form – y = mx + b
Step 1: Start at the y-intercept (0, b)
Step 2: Create a chain of stair-step of the rise (units up or down) and run (units to the right – never to the left since negative slopes go down not left). Place a dot after each step.
Step 3: Connect the dots with a line.
Method 2: Function Table
Step 1: Create a table consisting of 3 colums and at least 3 rows. Label each column “x”, “(equation)”, and “y”
Step 2: Create your own x values and place them in the “x” column (one per row). Tip: Use easy x values to substitute, like 0, 1, 2, -1, and -2.
Step 3: Plot each (x, y) pair.
Step 4: Connect the dots with a line.
ALGEBRA 1
“Slope-Intercept Form” (5-2)
Example: Graph y = -2x + 1.
Method 1: Slope-Intercept Form
Step 1: The y-intercept is 1, so start at (0,1)
Step 2: The slope is -2 or -2/1 which means a rise of -2 (down 2) and a run of 1 (right 1). Create a few stair-steps that go down 2 and right 1.
Step 3: Connect the dots with a line.
ALGEBRA 1
“Slope-Intercept Form” (5-2)
Example: Graph y = -2x + 1.
Method 2: Function Table
ALGEBRA 1
The base pay for a used car salesperson is $300 per
week. The salesperson also earns 15% commission on sales
made. The equation t = 300 + 0.15s relates total earnings t to sales
s. Graph the equation.
Step 1 Identify the slope and y-intercept.
t = 300 + 0.15s
t = 0.15s + 300 Rewrite the equation in slope intercept form.
slope y-intercept
Slope-Intercept FormLESSON 5-2
Additional Examples
ALGEBRA 1
Step 2 Plot two points. First plot a point at the y-intercept. Then use the
slope to plot a second point.
(continued)
Step 3 Draw a line through the points.
15 100
The slope is 0.15, which equals . Plot a second point 15 units above and
100 units to the right of the y-intercept.
Slope-Intercept FormLESSON 5-2
Additional Examples
ALGEBRA 1
m = –2; b = 0
y = 0.5x + 1
34
35
m = ; b = –334
y = – x – 435
Find the slope and y-intercept of each equation.
1. y = x – 3
2. y = –2x
Write an equation of a line with the given slope and y-intercept.
3. m = – , b = –4
4. m = 0.5, b = 1
Slope-Intercept FormLESSON 5-2
Lesson Quiz
ALGEBRA 1
5. Write an equation for the line.
6. Graph y = –x + 3.
y = x – 312
7. Determine whether (3, –7) lies on the graph of y = 4x – 5.
(3, –7) is not a solution
Slope-Intercept FormLESSON 5-2
Lesson Quiz