QuestionCalculate the slope of the line through points $(-1,2)$ and $(4,5)$ ; state if it rises, falls, horizontal, or vertical.

Studdy Solution

STEP 1

Assumptions1. We have two points in the Cartesian coordinate system $(-1,)$ and $(4,5)$ . The slope of a line passing through two points $(x1, y1)$ and $(x, y)$ can be calculated using the formula $slope = \frac{y - y1}{x - x1}$

STEP 2

Let's denote the given points as followsPoint1 $(-1,2)$ , so $x1 = -1$ and $y1 =2$
Point2 $(4,5)$ , so $x2 =4$ and $y2 =5$

STEP 3

Substitute the values of $x1$ , $y1$ , $x2$ , and $y2$ into the slope formula.
$slope = \frac{y2 - y1}{x2 - x1} = \frac{5 -2}{ - (-1)}$

STEP 4

implify the expression in the numerator and the denominator.
$slope = \frac{3}{}$

STEP 5

The slope of the line passing through the points $(-1,2)$ and $(4,5)$ is $\frac{3}{5}$ .
Since the slope is positive, the line rises from left to right.

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