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QuestionFind the linear equation of the line through the points (1,−6)(1,-6) and (−1,−1)(-1,-1). y(x)=y(x) =

Studdy Solution

STEP 1

Assumptions1. The line passes through the points (1,−6)(1,-6) and (−1,−1)(-1,-1). . The line is linear, meaning it can be represented by an equation of the form y=mx+cy = mx + c, where mm is the slope and cc is the y-intercept.

STEP 2

First, we need to find the slope of the line. The slope is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Now, plug in the given values for x1x1, y1y1, x2x2, and y2y2 to calculate the slope.
m=−1−(−6)−1−1m = \frac{-1 - (-6)}{-1 -1}

STEP 4

implify the equation to find the slope.
m=−1+6−1−1=−2=−2m = \frac{-1 +6}{-1 -1} = \frac{}{-2} = -\frac{}{2}

STEP 5

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

STEP 6

Plug in the values for mm, x1x1, and y1y1 to find the equation of the line.
y−(−6)=−52(x−1)y - (-6) = -\frac{5}{2}(x -1)

STEP 7

implify the equation to find the equation of the line.
y+6=−52x+52y +6 = -\frac{5}{2}x + \frac{5}{2}

STEP 8

Subtract6 from both sides to isolate yy.
y=−52x+52−6y = -\frac{5}{2}x + \frac{5}{2} -6

STEP 9

implify the equation to find the final equation of the line.
y=−52x−72y = -\frac{5}{2}x - \frac{7}{2}So, the linear equation whose graph is the straight line passing through the points (,−6)(,-6) and (−,−)(-,-) is y=−52x−72y = -\frac{5}{2}x - \frac{7}{2}.

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