Question

Use point-slope form to write the equation of the line in slope-intercept form that passes through the points (0, -5) and (-3, 4).

Slope formula: m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction

Point-slope form: y – y1 = m(x – x1)

Slope-intercept form: y = mx + b

Choose the equation of the line.
y = –3x – 13
y = –3x – 5
y = –3x + 5
y = Negative one-third x + 13

Answer 1

To find the equation of the line that passes through the points (0, -5) and (-3, 4), we start by calculating the slope using the slope formula.

Let \((x_1, y_1) = (0, -5)\) and \((x_2, y_2) = (-3, 4)\).

Using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - (-5)}{-3 - 0} = \frac{4 + 5}{-3} = \frac{9}{-3} = -3
\]

Now that we have the slope \(m = -3\), we can use the point-slope form to write the equation of the line:
\[
y - y_1 = m(x - x_1)
\]
Using point (0, -5):
\[
y - (-5) = -3(x - 0)
\]
This simplifies to:
\[
y + 5 = -3x
\]
\[
y = -3x - 5
\]

Now we have the equation in slope-intercept form \(y = mx + b\).

The final equation of the line is:
\[
y = -3x - 5
\]

Therefore, the correct choice among the options given is:
**y = -3x - 5**