Question

Use the table to answer the question.

x
y

−3
0
−2
3
−1
6
Write the equation of the line in slope-intercept form.

(1 point)

Answer 1

To find the equation of the line in slope-intercept form (\(y = mx + b\)), we need to calculate the slope (\(m\)) using the given points and then find the y-intercept (\(b\)).

Given the points:
1. \((-3, 0)\)
2. \((-2, 3)\)
3. \((-1, 6)\)

We can calculate the slope (\(m\)) using two points, for example, \((-3, 0)\) and \((-2, 3)\).

The formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using \((-3, 0)\) as \((x_1, y_1)\) and \((-2, 3)\) as \((x_2, y_2)\):
\[
m = \frac{3 - 0}{-2 - (-3)} = \frac{3}{1} = 3
\]

Now, we have the slope \(m = 3\).

Next, we need to find the y-intercept (\(b\)). We can use one of the points; let's use the point \((-2, 3)\) and the slope we found.

Substituting \(x\) and \(y\) into the slope-intercept equation:
\[
y = mx + b \implies 3 = 3(-2) + b
\]
\[
3 = -6 + b
\]
\[
b = 3 + 6 = 9
\]

Now we have both the slope and the y-intercept:
- Slope \(m = 3\)
- Y-intercept \(b = 9\)

The equation of the line in slope-intercept form is:
\[
y = 3x + 9
\]