Question

Points are -2,0. 0,6
Write the equation of this line in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To find the equation of the line that passes through the points \((-2, 0)\) and \((0, 6)\), we first need to determine the slope of the line and then use the slope-intercept form (which is \(y = mx + b\)), where \(m\) is the slope and \(b\) is the y-intercept.

**Step 1: Calculate the slope (m)**

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using the points \((-2, 0)\) and \((0, 6)\):

- \((x_1, y_1) = (-2, 0)\)
- \((x_2, y_2) = (0, 6)\)

Substituting these values into the slope formula:

\[
m = \frac{6 - 0}{0 - (-2)} = \frac{6}{0 + 2} = \frac{6}{2} = 3
\]

**Step 2: Use the slope and a point to find the y-intercept (b)**

We can use the point \((0, 6)\) to find \(b\) since the y-coordinate of this point is where the line crosses the y-axis:

\[
y = mx + b
\]

Substituting \(m = 3\), \(x = 0\), and \(y = 6\):

\[
6 = 3(0) + b
\]
\[
6 = b
\]

**Step 3: Write the equation in slope-intercept form**

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

\[
y = 3x + 6
\]

This is the equation of the line in slope-intercept form. Thus, the final answer is:

\[
y = 3x + 6
\]