Question

A line passes through the points (8,10)
and (13,17)
. What is the equation of the line in point-slope form?(1 point)
Responses

y+17=75(x+13)
y plus 17 equals Start Fraction 7 over 5 End Fraction left parenthesis x plus 13 right parenthesis

y−10=57(x−13)
y minus 10 equals Start Fraction 5 over 7 End Fraction left parenthesis x minus 13 right parenthesis

y−10=57(x−8)
y minus 10 equals Start Fraction 5 over 7 End Fraction left parenthesis x minus 8 right parenthesis

y−10=75(x−8)

Answer 1

To find the equation of the line in point-slope form that passes through the points (8, 10) and (13, 17), we first need to calculate the slope (m) of the line. The slope is given by the formula:

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

Using the points (8, 10) as \((x_1, y_1)\) and (13, 17) as \((x_2, y_2)\):

\[
m = \frac{17 - 10}{13 - 8} = \frac{7}{5}
\]

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

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

We can choose either point to use in the equation. We'll use (8, 10):

\[
y - 10 = \frac{7}{5}(x - 8)
\]

So the equation of the line in point-slope form is:

\[
\boxed{y - 10 = \frac{7}{5}(x - 8)}
\]

This matches the option:

**y−10=75(x−8)**.