Question

I need to know how to answer this Math equation

Answer 1

The slope of a line passing through two points A(x₁, y₁) and B(x₂, y₂) is expressed as

`\begin{gathered} \text{slope = }(rise)/(runs)=(y_2-y_1)/(x_2-x_1)_{} \\ \text{where} \\ (x_1,y_1)\Rightarrow coordinate\text{ of point A} \\ (x_2,y_2)\Rightarrow coordinate\text{ of point B} \end{gathered}`

The line through the given points rises, when the slope is positive;

The line through the given points is horizontal, when the slope equals zero;

The line through the given points is vertical when the slope is undefined;

The line through the given points falls, when the slope is negative.

Given the points (3,-2) and (5, 6).

`\begin{gathered} x_1=3 \\ y_1=-2 \\ x_2=5 \\ y_2=6 \end{gathered}`

thus, the slope is evaluated as

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1)=(6-(-2))/(5-3)=(6+2)/(5-3)=(8)/(2) \\ \Rightarrow slope=4 \end{gathered}`

Hence, the slope passing through the points (3,-2) and (5, 6) is 4.

Since the obtained slope is positive, the line through the points (3,-2) and (5, 6) rises.