Math

QuestionFind the slope of the line through points (5,3)(-5,3) and (3,6)(3,6) and state if it rises, falls, is horizontal, or vertical.

Studdy Solution

STEP 1

Assumptions1. We have two points in the Cartesian plane (5,3)(-5,3) and (3,6)(3,6). . We need to find the slope of the line passing through these points.
3. If the denominator of the slope calculation is zero, the slope is undefined.
4. The line rises if the slope is positive, falls if the slope is negative, is horizontal if the slope is zero, and is vertical if the slope is undefined.

STEP 2

The slope of a line passing through two points (x1,y1)(x1, y1) and (x2,y2)(x2, y2) is given by the formulam=y2y1x2x1m = \frac{y2 - y1}{x2 - x1}

STEP 3

Plug in the given values for x1x1, y1y1, x2x2, and y2y2 into the formula.
m=633(5)m = \frac{6 -3}{3 - (-5)}

STEP 4

implify the expression in the numerator and denominator.
m=38m = \frac{3}{8}

STEP 5

The slope of the line is 38\frac{3}{8}, which is a positive number. Therefore, the line rises.
The slope of the line passing through the points (5,3)(-5,3) and (3,)(3,) is 38\frac{3}{8} and the line rises.

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