The graph of a function is a straight line with a slope of 2 and a y

Question

-intercept of 7. What is the equation of the function? Write your answer in y=mx+b
form.(1 point)
The equation of a function is y=−7x−12
. If this function were graphed, what would its slope be?(1 point)
Use the table to answer the question.

x
y

11 58
20 103
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b
form.

(1 point)
Use the image to answer the question.

An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 6 to 6 in one unit increments. The y-axis ranges from negative 4 to 6 in one unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis negative 3 comma negative 1 right parenthesis and left parenthesis 2 comma 4 right parenthesis.

Write the equation of the linear function shown on the graph. Enter your answer in y=mx+b
form.

(1 point)
Yesterday, Esperanza worked for 6 hours and earned $120. Today, Esperanza worked 8 hours and earned $156. Write the equation of the linear function that models the relationship between the number of hours Esperanza works and the amount of money she earns. Enter your answer in y=mx+b
form.(1 point)

Answer 1

Let's go through each question one by one.

1. Equation of the function based on slope and y-intercept: The slope (m) is 2, and the y-intercept (b) is 7. The equation in the form \( y = mx + b \) is: \[ y = 2x + 7 \]

2. Slope of the function \( y = -7x - 12 \): The slope (m) of the given equation is the coefficient of x. So, the slope is: \[ m = -7 \]

3. Writing the equation of the linear function from the table: To find the slope (m) from the two points (11, 58) and (20, 103), we use the formula for slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{103 - 58}{20 - 11} = \frac{45}{9} = 5 \] Now we can use one of the points (let's use (11, 58)) to find the y-intercept (b): \[ y = mx + b \implies 58 = 5(11) + b \implies 58 = 55 + b \implies b = 3 \] Therefore, the equation of the linear function is: \[ y = 5x + 3 \]

4. Writing the equation of the linear function from the graph: First, we calculate the slope (m) from the points (-3, -1) and (2, 4): \[ m = \frac{4 - (-1)}{2 - (-3)} = \frac{4 + 1}{2 + 3} = \frac{5}{5} = 1 \] Now, using one of the points (let's use (-3, -1)) to find the y-intercept (b): \[ y = mx + b \implies -1 = 1(-3) + b \implies -1 = -3 + b \implies b = 2 \] Therefore, the equation of the linear function is: \[ y = x + 2 \]

5. Writing the equation for Esperanza's earnings based on hours worked: To find the slope (m) we can calculate it based on the hours and earnings: \[ m = \frac{156 - 120}{8 - 6} = \frac{36}{2} = 18 \] Now, we can use one of the points (let's use (6, 120)) to find the y-intercept (b): \[ y = mx + b \implies 120 = 18(6) + b \implies 120 = 108 + b \implies b = 12 \] Therefore, the equation of the linear function is: \[ y = 18x + 12 \]

In summary:

1. \( y = 2x + 7 \)
2. Slope is \( -7 \)
3. \( y = 5x + 3 \)
4. \( y = x + 2 \)
5. \( y = 18x + 12 \)