Question

What is an equation of the line that passes through the points left parenthesis, 1, comma, 7, right parenthesis(1,7) and left parenthesis, minus, 1, comma, minus, 1, right parenthesis(−1,−1)?

Answer 1

To find the equation of the line that passes through the points \( (1, 7) \) and \( (-1, -1) \), we can use the point-slope form of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \( m \) is the slope of the line and \( (x_1, y_1) \) is one of the points.

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

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

Using the points \( (x_1, y_1) = (1, 7) \) and \( (x_2, y_2) = (-1, -1) \):

\[
m = \frac{-1 - 7}{-1 - 1} = \frac{-8}{-2} = 4
\]

Now that we have the slope \( m = 4 \), we can use one of the points to write the equation. We'll use the point \( (1, 7) \):

\[
y - 7 = 4(x - 1)
\]

Expanding this, we get:

\[
y - 7 = 4x - 4
\]

Adding 7 to both sides:

\[
y = 4x + 3
\]

Thus, the equation of the line that passes through the points \( (1, 7) \) and \( (-1, -1) \) is:

\[
y = 4x + 3
\]