Math

QuestionFind the equation of the line through the points (3,9)(-3,-9) and (5,9)(5,-9).

Studdy Solution

STEP 1

Assumptions1. The line passes through the points (3,9)(-3,-9) and (5,9)(5,-9). The equation of a line in slope-intercept form is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept

STEP 2

First, we need to find the slope of the line. The slope of a line passing through two points (x1,y1)(x1, y1) and (x2,y2)(x2, y2) is given bym=y2y1x2x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Now, plug in the given values for the points to calculate the slope.
m=9(9)5(3)m = \frac{-9 - (-9)}{5 - (-3)}

STEP 4

implify the equation to calculate the slope.
m=08=0m = \frac{0}{8} =0

STEP 5

The slope of the line is0, which means the line is horizontal. For a horizontal line, the equation is of the form y=by = b, where bb is the y-coordinate of any point on the line.

STEP 6

We can use either of the given points to find the value of bb. Let's use the point (3,9)(-3,-9).
b=9b = -9

STEP 7

Substitute the value of bb into the equation of the line.
y=9y = -9The equation of the line that passes through the points (3,9)(-3,-9) and (5,9)(5,-9) is y=9y = -9.

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