Question

Use the table to answer the question.

x
y

1 −5

2 0
3 5
Write the equation of the line in slope-intercept form.

Answer 1

To find the equation of the line in slope-intercept form \(y = mx + b\), we first need to determine the slope \(m\) using the given points from the table:

The points are:
1. \( (1, -5) \)
2. \( (2, 0) \)
3. \( (3, 5) \)

The slope \(m\) can be calculated using the formula:

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

We can choose any two points. Let's take points \((1, -5)\) and \((2, 0)\):

\[
m = \frac{0 - (-5)}{2 - 1} = \frac{5}{1} = 5
\]

Now that we have the slope \(m = 5\), we can use one of the points to find the y-intercept \(b\).

Let's use the point \((2, 0)\):

Substituting \(x = 2\) and \(y = 0\) into the slope-intercept form:

\[
0 = 5(2) + b
\]
\[
0 = 10 + b
\]
\[
b = -10
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = 5x - 10
\]