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Math  /  Algebra

QuestionFind the slope of the line through each pair of points. 3) (−3,−9),(12,19)(-3,-9),(12,19) 4) (−16,10),(11,16)(-16,10),(11,16)
Find the slope of each line. 5) y=−x+4y=-x+4 6) y=−2x+2y=-2 x+2
Find the slope of a line parallel to each given line. 7) y=6x+4y=6 x+4 8) y=4y=4
Find the slope of a line perpendicular to each given line. 10) x=2x=2 9) y=12x+1y=\frac{1}{2} x+1

Studdy Solution

STEP 1

1. The slope of a line through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1} .
2. The slope of a line in the form y=mx+b y = mx + b is m m .
3. Lines that are parallel have the same slope.
4. Lines that are perpendicular have slopes that are negative reciprocals of each other.

STEP 2

1. Calculate the slope of the line through each pair of points.
2. Identify the slope of each given line.
3. Determine the slope of a line parallel to each given line.
4. Determine the slope of a line perpendicular to each given line.

STEP 3

Calculate the slope for points (−3,−9)(-3, -9) and (12,19)(12, 19):
m=19−(−9)12−(−3)=19+912+3=2815 m = \frac{19 - (-9)}{12 - (-3)} = \frac{19 + 9}{12 + 3} = \frac{28}{15}

STEP 4

Calculate the slope for points (−16,10)(-16, 10) and (11,16)(11, 16):
m=16−1011−(−16)=611+16=627=29 m = \frac{16 - 10}{11 - (-16)} = \frac{6}{11 + 16} = \frac{6}{27} = \frac{2}{9}

STEP 5

Identify the slope of the line y=−x+4 y = -x + 4 :
The slope m=−1 m = -1 .

STEP 6

Identify the slope of the line y=−2x+2 y = -2x + 2 :
The slope m=−2 m = -2 .

STEP 7

Determine the slope of a line parallel to y=6x+4 y = 6x + 4 :
The slope of a parallel line is the same, m=6 m = 6 .

STEP 8

Determine the slope of a line parallel to y=4 y = 4 :
The line y=4 y = 4 is horizontal, so the slope of a parallel line is m=0 m = 0 .

STEP 9

Determine the slope of a line perpendicular to y=12x+1 y = \frac{1}{2}x + 1 :
The slope of a perpendicular line is the negative reciprocal, m=−2 m = -2 .

STEP 10

Determine the slope of a line perpendicular to x=2 x = 2 :
The line x=2 x = 2 is vertical, so the slope of a perpendicular line is m=0 m = 0 .

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