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

Question

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.