Question

What is an equation of the line that passes through the points left parenthesis, 2, comma, 8, right parenthesis(2,8) and left parenthesis, minus, 8, comma, minus, 7, right parenthesis(−8,−7)?

Answer 1

What is an equation of the line that passes through the points left parenthesis, minus, 3, comma, minus, 5, right parenthesis(−3,−5) and left parenthesis, minus, 2, comma, minus, 4, right parenthesis(−2,−4)?

Answer 2

To find the equation of a line that passes through the points \((2, 8)\) and \((-8, -7)\), we can start by calculating the slope \(m\) of the line. The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

In this case, let \((x_1, y_1) = (2, 8)\) and \((x_2, y_2) = (-8, -7)\). Plugging in these values:

\[
m = \frac{-7 - 8}{-8 - 2} = \frac{-15}{-10} = \frac{3}{2}
\]

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

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

Using the point \((2, 8)\) and the slope \(m = \frac{3}{2}\):

\[
y - 8 = \frac{3}{2}(x - 2)
\]

Now we can simplify this equation:

1. Distribute \(\frac{3}{2}\):

\[
y - 8 = \frac{3}{2}x - 3
\]

2. Add \(8\) to both sides:

\[
y = \frac{3}{2}x - 3 + 8
\]

\[
y = \frac{3}{2}x + 5
\]

Thus, the equation of the line that passes through the points \((2, 8)\) and \((-8, -7)\) in slope-intercept form is:

\[
y = \frac{3}{2}x + 5
\]