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QuestionFind the slope of the line through points A(4,−3)A(4,-3) and B(−4,−1)B(-4,-1), then determine the y-intercept as an ordered pair.

Studdy Solution

STEP 1

Assumptions1. The coordinates of point A are (4, -3) . The coordinates of point B are (-4, -1)
3. We are looking for the slope of the line passing through these points4. We are also looking for the y-intercept of the line

STEP 2

The formula for finding the slope (m) of a line given two points A(x1, y1) and B(x2, y2) ism=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Substitute the given coordinates of points A and B into the formulam=−1−(−3)−−m = \frac{-1 - (-3)}{- -}

STEP 4

implify the equationm=−1+3−4−4=2−8m = \frac{-1 +3}{-4 -4} = \frac{2}{-8}

STEP 5

Calculate the slopem=2−8=−14m = \frac{2}{-8} = -\frac{1}{4}So, the slope of the line passing through points A and B is -1/4.

STEP 6

The equation of a line is given byy=mx+cy = mx + cwhere m is the slope and c is the y-intercept.

STEP 7

To find the y-intercept (c), we can substitute the slope (m) and the coordinates of one of the points into the equation of the line. Let's use point A(4, -3):
−3=−14⋅4+c-3 = -\frac{1}{4} \cdot4 + c

STEP 8

implify the equation−3=−1+c-3 = -1 + c

STEP 9

olve for c (the y-intercept):
c=−3+=−2c = -3 + = -2So, the y-intercept of the line is -2.

STEP 10

Express the y-intercept as an ordered pair (0, c):
The y-intercept is (0, -2).
So, the slope of the line passing through points A(4, -3) and B(-4, -) is -/4, and the y-intercept of the line is (0, -2).

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