Math / Algebra

QuestionLines Finding slope given the graph of a line in quadrant 1 that models a real-...
Keisha makes house calls. For each, she is paid a base amount and makes additional money for each hour she works. The graph below. shows her pay (i dollars) versus the number of hours worked.
Use the graph to answer the questions. (a) How much does her pay increase for each hour worked? \\square$ (h) What is the slone of the line?

Studdy Solution

STEP 1

1. The graph represents a linear relationship between hours worked and pay.
2. The line passes through the points (0, 20) and (8, 180).
3. The slope of the line represents the rate of change of pay per hour worked.

STEP 2

1. Identify the points on the graph.
2. Use the slope formula to calculate the slope.
3. Interpret the slope in the context of the problem.

STEP 3

Identify the points on the graph. The line passes through the points $(0, 20)$ and $(8, 180)$ .

STEP 4

Use the slope formula to calculate the slope. The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the points $(0, 20)$ and $(8, 180)$ into the formula:
$m = \frac{180 - 20}{8 - 0}$

STEP 5

Simplify the expression:
$m = \frac{160}{8}$ $m = 20$

STEP 6

Interpret the slope in the context of the problem. The slope of the line, $20$ , represents the increase in pay for each additional hour worked. Therefore, Keisha's pay increases by \$20 for each hour worked.
Solution: (a) Keisha's pay increases by \$20 for each hour worked. (h) The slope of the line is $ 20 $.

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Studdy Solution

STEP 1

1. The graph represents a linear relationship between hours worked and pay.
2. The line passes through the points (0, 20) and (8, 180).
3. The slope of the line represents the rate of change of pay per hour worked.

STEP 2

1. Identify the points on the graph.
2. Use the slope formula to calculate the slope.
3. Interpret the slope in the context of the problem.

STEP 3

Identify the points on the graph. The line passes through the points $(0, 20)$ and $(8, 180)$ .

STEP 4

Use the slope formula to calculate the slope. The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the points $(0, 20)$ and $(8, 180)$ into the formula:
$m = \frac{180 - 20}{8 - 0}$

STEP 5

Simplify the expression:
$m = \frac{160}{8}$ $m = 20$

STEP 6

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Studdy Solution

STEP 1

1. The graph represents a linear relationship between hours worked and pay.2. The line passes through the points (0, 20) and (8, 180).3. The slope of the line represents the rate of change of pay per hour worked.

STEP 2

1. Identify the points on the graph.2. Use the slope formula to calculate the slope.3. Interpret the slope in the context of the problem.

STEP 3

Identify the points on the graph. The line passes through the points (0,20) (0, 20) (0,20) and (8,180) (8, 180) (8,180).

STEP 4

STEP 5

Simplify the expression:m=1608 m = \frac{160}{8} m=8160​ m=20 m = 20 m=20

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The graph represents a linear relationship between hours worked and pay.
2. The line passes through the points (0, 20) and (8, 180).
3. The slope of the line represents the rate of change of pay per hour worked.

1. Identify the points on the graph.
2. Use the slope formula to calculate the slope.
3. Interpret the slope in the context of the problem.

Identify the points on the graph. The line passes through the points $(0, 20)$ and $(8, 180)$ .

Simplify the expression:
$m = \frac{160}{8}$ $m = 20$