Question

if a line passes through the points (2, 4) and (6, 8), what is the slope?
a. 4
b. 1
c. \\(\frac{1}{2}\\)
d. 2

a positive slope means the line is:
a. horizontal
b. vertical
c. falling from left to right
d. rising from left to right

Explanation:

First Sub - Question (Slope Calculation)

Step 1: Recall the slope formula

The formula for the slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step 2: Identify the points

Here, \((x_1,y_1)=(2,4)\) and \((x_2,y_2)=(6,8)\).

Step 3: Substitute into the formula

Substitute the values into the slope formula: \(m=\frac{8 - 4}{6 - 2}=\frac{4}{4}=1\).

A horizontal line has a slope of 0, a vertical line has an undefined slope. A positive slope means that as \(x\) (the horizontal axis) increases (moving from left to right), \(y\) (the vertical axis) also increases, so the line is rising from left to right. A negative slope would mean the line is falling from left to right.

Answer:

b. 1

Second Sub - Question (Interpretation of Positive Slope)