Question

Write the equation of the linear function shown on the graph. Enter your answer in y=mx+b form. The graph is positive, with the points (-3,1) and (2,4)

Answer 1

its wrong.

Answer 2

To find the equation of the linear function represented by the points (-3, 1) and (2, 4), we'll follow these steps:

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1) = (-3, 1)\) and \((x_2, y_2) = (2, 4)\).

Substituting the values:
\[
m = \frac{4 - 1}{2 - (-3)} = \frac{3}{2 + 3} = \frac{3}{5}
\]

2. **Use the point-slope form of the equation** with one of the points. We can use the point (-3, 1):
\[
y - y_1 = m(x - x_1)
\]
Substituting \(m\), \(x_1\), and \(y_1\):
\[
y - 1 = \frac{3}{5}(x + 3)
\]

3. **Simplify this to slope-intercept form (y = mx + b)**:
- Distribute \(\frac{3}{5}\):
\[
y - 1 = \frac{3}{5}x + \frac{9}{5}
\]
- Add 1 (which is \(\frac{5}{5}\)) to both sides:
\[
y = \frac{3}{5}x + \frac{9}{5} + \frac{5}{5}
\]
\[
y = \frac{3}{5}x + \frac{14}{5}
\]

Thus, the equation of the linear function is:
\[
y = \frac{3}{5}x + \frac{14}{5}
\]