Question

A chart shows 2 points, one at (25, 100) and another (10, 70).

Write the equation of the linear function shown on the graph.

(1 point)
Responses

y=12x−25
y
=
1
2
x
−
25
y equals Start Fraction 1 over 2 End Fraction x minus 25

y=2x+50
y
=
2
x
+
50
y equals 2 x plus 50

y=12x+50
y
=
1
2
x
+
50
y equals Start Fraction 1 over 2 End Fraction x plus 50

y=2x−25

Answer 1

To find the equation of the linear function that passes through the points (25, 100) and (10, 70), we can follow these steps:

1. **Find the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plugging in the coordinates of the two points:
\[
m = \frac{70 - 100}{10 - 25} = \frac{-30}{-15} = 2
\]

2. **Use the slope-intercept form** of the equation of a line, which is:
\[
y = mx + b
\]

3. **Substitute the slope into the equation** and use one of the points to find b (the y-intercept). Let's use the point (25, 100):
\[
100 = 2(25) + b
\]
\[
100 = 50 + b
\]
\[
b = 100 - 50 = 50
\]

4. **Write the final equation**:
\[
y = 2x + 50
\]

So the correct response is:
**y = 2x + 50**.