Question

A line passes through the points (7.5,−2)
and (−5,8)
. What is the equation of the line in slope-intercept form?(1 point)
Responses

y=−45x+4
y equals negative Start Fraction 4 over 5 End Fraction x plus 4

y=45x+4
y equals Start Fraction 4 over 5 End Fraction x plus 4

y=54x+4
y equals Start Fraction 5 over 4 End Fraction x plus 4

y=54x−2

Answer 1

To find the equation of the line that passes through the points (7.5, -2) and (-5, 8), we first need to calculate the slope (m) using the formula:

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

Let \((x_1, y_1) = (7.5, -2)\) and \((x_2, y_2) = (-5, 8)\).

Plugging in the values:

\[
m = \frac{8 - (-2)}{-5 - 7.5} = \frac{8 + 2}{-5 - 7.5} = \frac{10}{-12.5} = -\frac{4}{5}
\]

Now that we have the slope \( m = -\frac{4}{5} \), we can use the point-slope form of the equation of a line, which is:

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

Choosing the point (7.5, -2):

\[
y - (-2) = -\frac{4}{5}(x - 7.5)
\]
\[
y + 2 = -\frac{4}{5}x + \frac{30}{5}
\]
\[
y + 2 = -\frac{4}{5}x + 6
\]
\[
y = -\frac{4}{5}x + 6 - 2
\]
\[
y = -\frac{4}{5}x + 4
\]

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

\[
y = -\frac{4}{5}x + 4
\]

The correct response is:

**y equals negative Start Fraction 4 over 5 End Fraction x plus 4**.