Question

What equation explains this line?

(-2,4) (1,13)

Answer 1

To find the equation of the line that passes through the points \((-2, 4)\) and \( (1, 13)\), we can use the slope-intercept form of a linear equation, which is given by:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Calculate the slope \(m\)

The slope \(m\) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-2, 4)\) and \( (1, 13)\):

- \(x_1 = -2, y_1 = 4\)
- \(x_2 = 1, y_2 = 13\)

Substituting these values into the slope formula:

\[
m = \frac{13 - 4}{1 - (-2)} = \frac{9}{3} = 3
\]

### Step 2: Use one of the points to find the y-intercept \(b\)

Now that we have the slope, we can use one of the points to find the y-intercept \(b\). We can use the point \((-2, 4)\):

\[
y = mx + b
\]
Substituting in \(m = 3\), \(x = -2\), and \(y = 4\):

\[
4 = 3(-2) + b
\]
\[
4 = -6 + b
\]
\[
b = 4 + 6 = 10
\]

### Final equation

Now that we have \(m\) and \(b\), we can write the equation of the line:

\[
y = 3x + 10
\]

This is the equation that explains the line passing through the points \((-2, 4)\) and \( (1, 13)\).