Use the image to answer the question. Write the equation of the linear function shown on the graph.

(25,100)
(10,70)

a. y = 1/2x + 50
b. y = 2x - 25
c. y = 1/2x - 25
d. y = 2x + 50

1 answer

To find the equation of the linear function given two points, we can use the slope-intercept form of a linear equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

  1. Identify the points: The points given are (25, 100) and (10, 70).

  2. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{70 - 100}{10 - 25} = \frac{-30}{-15} = 2 \]

  3. Use the slope and one of the points to find b: Using the slope \( m = 2 \) and the point (10, 70): \[ y = mx + b \rightarrow 70 = 2(10) + b \rightarrow 70 = 20 + b \rightarrow b = 70 - 20 = 50 \]

  4. Write the equation: Putting it all together, we have: \[ y = 2x + 50 \]

Therefore, the equation of the linear function shown on the graph is:

d. y = 2x + 50