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).

Question

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