Question

Write the equation of the linear function of (10,70)(25,100)

Answer 1

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

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (10, 70)\) and \((x_2, y_2) = (25, 100)\).

Plugging in the values:
\[
m = \frac{100 - 70}{25 - 10} = \frac{30}{15} = 2
\]

2. **Use the point-slope form of the equation**:
The point-slope form is given by:
\[
y - y_1 = m(x - x_1)
\]
Using the slope \(m = 2\) and point \((10, 70)\):
\[
y - 70 = 2(x - 10)
\]

3. **Convert to slope-intercept form (y = mx + b)**:
Distributing and rearranging:
\[
y - 70 = 2x - 20
\]
\[
y = 2x + 50
\]

Thus, the equation of the linear function is:
\[
\boxed{y = 2x + 50}
\]