Question

What is an equation in point-slope form for the line that passes through the points (−3,5)
and (2,−3) ?



y−5=−85(x+3)
y minus 5 equals negative fraction 8 over 5 end fraction open parenthesis x plus 3 close parenthesis

y−3=−85(x+5)
y minus 3 equals negative fraction 8 over 5 end fraction open parenthesis x plus 5 close parenthesis

y−3=−58(x+5)
y minus 3 equals negative fraction 5 over 8 end fraction open parenthesis x plus 5 close parenthesis

y−5=85(x+3)

Answer 1

To find the equation of the line in point-slope form that passes through the points (−3, 5) and (2, −3), we first need to calculate the slope \( m \) of the line using the slope formula:

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

Where \((x_1, y_1) = (-3, 5)\) and \((x_2, y_2) = (2, -3)\).

Substituting the values into the slope formula:

\[
m = \frac{-3 - 5}{2 - (-3)} = \frac{-8}{2 + 3} = \frac{-8}{5}
\]

So, the slope \( m = -\frac{8}{5} \).

Now we can write the point-slope form of the line, which is given by:

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

We can choose either of the two points. Let's use point \((-3, 5)\):

\[
y - 5 = -\frac{8}{5}(x + 3)
\]

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

\[
y - 5 = -\frac{8}{5}(x + 3)
\]

So, the first option you provided is correct:

\[
y - 5 = -\frac{8}{5}(x + 3)
\]