Question

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

y−10=75(x−8)
y
−
10
=
7
5
(
x
−
8
)
y minus 10 equals Start Fraction 7 over 5 End Fraction left parenthesis x minus 8 right parenthesis

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

y+17=75(x+13)
y
+
17
=
7
5
(
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)

Answer 1

To find the equation of the line in point-slope form, we first need to determine the slope of the line using the two points (8, 10) and (13, 17).

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

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

Substituting in the given points:

- \( (x_1, y_1) = (8, 10) \)
- \( (x_2, y_2) = (13, 17) \)

We have:

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

Now that we have the slope \( m = \frac{7}{5} \), we can use the point-slope form of a line equation, which is:

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

Using the point (8, 10):

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

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

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

So the correct answer is:

**y−10=75(x−8)**