Question

A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line?
y = negative one-fifth x + 1
y = one-fifth x + 3
y = –5x – 23
y = 5x + 27

Answer 1

To find the equation of the line that passes through the points (-5, 2) and (10, -1), we can use the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

First, we need to calculate the slope \( m \) using the formula:

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

Using the points \((-5, 2)\) (let's call this \((x_1, y_1)\)) and \((10, -1)\) (let's call this \((x_2, y_2)\)), we get:

\[
m = \frac{-1 - 2}{10 - (-5)} = \frac{-3}{15} = -\frac{1}{5}
\]

Now that we have the slope \( m = -\frac{1}{5} \), we can use one of the points to find the y-intercept \( b \). We'll use the point (-5, 2).

Substituting into the equation:

\[
y = mx + b
\]
\[
2 = -\frac{1}{5}(-5) + b
\]

This simplifies to:

\[
2 = 1 + b
\]
\[
b = 2 - 1 = 1
\]

Now we can write the equation of the line:

\[
y = -\frac{1}{5}x + 1
\]

Looking at the options given, the correct equation matches:

\[
y = -\frac{1}{5}x + 1
\]

Hence, the answer is:

**None of the provided options are correct. The equation of the line is \( y = -\frac{1}{5}x + 1 \).**