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Use the work shown below to write the equation for a line that passes through the points (−5, 0) and (−1, −8).

1. Use slope formula to find slope:

m = StartFraction negative 8 minus 0 Over negative 1 minus (negative 5) EndFraction = StartFraction negative 8 Over 4 EndFraction = negative 2

2. Substitute one point and slope into slope-intercept form to find the y-intercept:

0 = negative 2 (negative 5) + b. 0 = 10 + b. b = negative 10.

What is the equation of the line in slope-intercept form?
y = –10x – 2
y = –1x – 8
–8 = –2x – 1
y = –2x – 10

1 answer

The work shown correctly calculates the slope and y-intercept for the line passing through the points (−5, 0) and (−1, −8).

  1. The slope (\(m\)) was found to be: \[ m = \frac{-8 - 0}{-1 - (-5)} = \frac{-8}{4} = -2 \]

  2. The y-intercept (\(b\)) is found by substituting one of the points (let's use \((-5, 0)\)) into the slope-intercept form (\(y = mx + b\)): \[ 0 = -2(-5) + b \] \[ 0 = 10 + b \] \[ b = -10 \]

Putting the slope and y-intercept together, the equation of the line in slope-intercept form is: \[ y = -2x - 10 \]

So the correct answer is: \[ y = -2x - 10 \]