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Math  /  Algebra

QuestionChoose the point-slope form of the equation below that represents the line that passes through the points (−3,2)(-3,2) and (2,1)(2,1). (2 points) 1) y+3=−5(x−2)y+3=-5(x-2) 2) y−2=−5(x+3)y-2=-5(x+3) 3) y+3=−15(x−2)y+3=-\frac{1}{5}(x-2) 4) y−2=−15(x+3)y-2=-\frac{1}{5}(x+3)

Studdy Solution

STEP 1

1. We are given two points: (−3,2)(-3, 2) and (2,1) (2, 1) .
2. We need to find the point-slope form of the equation of the line passing through these points.
3. The point-slope form of a line is given by y−y1=m(x−x1) y - y_1 = m(x - x_1) , where m m is the slope and (x1,y1)(x_1, y_1) is a point on the line.

STEP 2

1. Calculate the slope of the line.
2. Use the point-slope form with one of the given points.
3. Match the equation with the given options.

STEP 3

Calculate the slope m m using the formula:
m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the points (−3,2)(-3, 2) and (2,1) (2, 1) :
m=1−22−(−3)=−15m = \frac{1 - 2}{2 - (-3)} = \frac{-1}{5}

STEP 4

Using the point-slope form y−y1=m(x−x1) y - y_1 = m(x - x_1) with the point (−3,2)(-3, 2):
y−2=−15(x+3)y - 2 = -\frac{1}{5}(x + 3)

STEP 5

Compare the derived equation y−2=−15(x+3) y - 2 = -\frac{1}{5}(x + 3) with the given options:
Option 4: y−2=−15(x+3) y - 2 = -\frac{1}{5}(x + 3)
The equation matches option 4.
The correct point-slope form of the equation is:
y−2=−15(x+3) \boxed{y - 2 = -\frac{1}{5}(x + 3)}

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