Question

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

Answer 1

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**