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QuestionFind which point among A. (−9,−65)(-9,-65), B. (−1,7)(-1,7), C. (0,8)(0,8), D. (−2,12)(-2,12), E. (7,17)(7,17) lies on the line through (−3,13)(-3,13) and (3,−5)(3,-5).

Studdy Solution

STEP 1

Assumptions1. The points (−3,13)(-3,13) and (3,−5)(3,-5) are on the line. . We need to find which other point is also on the same line.

STEP 2

First, we need to find the slope of the line that passes through the points (−,13)(-,13) and (,−5)(,-5). The formula for the slope (m) between two points (x1,y1)(x1, y1) and (x2,y2)(x2, y2) ism=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Now, plug in the given values for the points into the slope formula.
m=−5−133−(−3)m = \frac{-5 -13}{3 - (-3)}

STEP 4

implify the expression to calculate the slope.
m=−186m = \frac{-18}{6}

STEP 5

Calculate the slope.
m=−3m = -3

STEP 6

Now that we have the slope, we can find the equation of the line using the point-slope form, which is y−y1=m(x−x1)y - y1 = m(x - x1), where (x1,y1)(x1, y1) is a point on the line and m is the slope. We can use the point (−3,13)(-3,13).

STEP 7

Plug in the values for the slope and the point into the point-slope form to get the equation of the line.
y−13=−3(x−(−3))y -13 = -3(x - (-3))

STEP 8

implify the equation to get it in the form y=mx+by = mx + b, where m is the slope and b is the y-intercept.
y=−3x+22y = -3x +22

STEP 9

Now that we have the equation of the line, we can check which of the given points satisfy this equation. That is, for a point (x,y)(x, y) to be on the line, it must satisfy the equation y=−3x+22y = -3x +22.

STEP 10

Check the point (−9,−65)(-9,-65).
−65=−3(−9)+22-65 = -3(-9) +22

STEP 11

implify the expression.
−65=27+22-65 =27 +22

STEP 12

Calculate the right side of the equation.
−65=49-65 =49Since −65≠49-65 \neq49, the point (−9,−65)(-9,-65) is not on the line.

STEP 13

Check the point (−,7)(-,7).
7=−3(−)+227 = -3(-) +22

STEP 14

implify the expression.
7=3+227 =3 +22

STEP 15

Calculate the right side of the equation.
7=257 =25Since 7≠257 \neq25, the point (−,7)(-,7) is not on the line.

STEP 16

Check the point (0,8)(0,8).
8=−3(0)+228 = -3(0) +22

STEP 17

implify the expression.
=22 =22Since ≠22 \neq22, the point (0,)(0,) is not on the line.

STEP 18

Check the point (−2,12)(-2,12).
12=−3(−2)+2212 = -3(-2) +22

STEP 19

implify the expression.
12=6+2212 =6 +22

STEP 20

Calculate the right side of the equation.
12=2812 =28Since 12≠2812 \neq28, the point (−,12)(-,12) is not on the line.

STEP 21

Check the point (7,17)(7,17).
17=−3(7)+17 = -3(7) +

STEP 22

implify the expression.
17=−21+2217 = -21 +22

STEP 23

Calculate the right side of the equation.
17=117 =1Since 17≠117 \neq1, the point (7,17)(7,17) is not on the line.
Therefore, none of the given points are on the line.

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