Question

page 12 of 12
Versions of Linear Equations Quick Check
5 of 55 of 5 Items
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=−4/5x+4
y equals negative Start Fraction 4 over 5 End Fraction x plus 4

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

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

y=5/4x−2

Answer 1

To find the equation of the line that passes through the points \((7.5, -2)\) and \((-5, 8)\) in slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), we first need to calculate the slope (\(m\)).

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

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

Calculating the slope:

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

Now we have the slope \(m = -\frac{4}{5}\).

Next, we can use either point to find the y-intercept \(b\) using the slope-intercept form \(y = mx + b\). Using the point \((7.5, -2)\):

\[
-2 = -\frac{4}{5}(7.5) + b
\]

Calculating \(-\frac{4}{5}(7.5)\):

\[
-\frac{4}{5} \cdot 7.5 = -6
\]

So we have:

\[
-2 = -6 + b
\]

Solving for \(b\):

\[
b = -2 + 6 = 4
\]

Now we can write the equation of the line:

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

From the given options, the correct response that matches this equation (in slope-intercept form) is:

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