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QuestionFind the line equation through points (−3,−6)(-3,-6) and (−1,−7)(-1,-7). Use slope-intercept or general form.

Studdy Solution

STEP 1

Assumptions1. We have two points given (−3,−6)(-3,-6) and (−1,−7)(-1,-7). We need to find the equation of the line passing through these points3. The equation of a line can be written in the form y=mx+cy = mx + c (slope-intercept form) or Ax+By+C=0Ax + By + C =0 (general form)

STEP 2

First, we need to find the slope of the line. The slope (m) of a line passing through two points (x1,y1)(x1, y1) and (x2,y2)(x2, y2) is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Now, plug in the given values for the points to calculate the slope.
m=−7−(−6)−1−(−3)m = \frac{-7 - (-6)}{-1 - (-3)}

STEP 4

implify the expression to find the slope.
m=−12=−0.m = \frac{-1}{2} = -0.

STEP 5

Now that we have the slope of the line, we can use the point-slope form of the equation of a line to find the equation. The point-slope form is given byy−y1=m(x−x1)y - y1 = m(x - x1)

STEP 6

Plug in the values for the slope and one of the points (let's use (−3,−6)(-3,-6)) to find the equation of the line.
y−(−6)=−0.5(x−(−3))y - (-6) = -0.5(x - (-3))

STEP 7

implify the equation to find the equation of the line.
y+6=−0.5x−1.5y +6 = -0.5x -1.5

STEP 8

Rearrange the equation to the slope-intercept form (y=mx+cy = mx + c).
y=−0.5x−1.5−6y = -0.5x -1.5 -6

STEP 9

implify the equation to find the final equation of the line.
y=−.5x−7.5y = -.5x -7.5So, the equation of the line passing through the points (−3,−6)(-3,-6) and (−,−7)(-,-7) is y=−.5x−7.5y = -.5x -7.5.

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