Question

3 the graph below shows a negative slope slope.

m = -1/2

b = 3

equation of the line that would be perpendicular: y = 2x+3

Explanation:

Step1: Identify slope of original line

The original line has slope \( m = -\frac{1}{2} \).

Step2: Recall perpendicular slope rule

Perpendicular slopes are negative reciprocals. So, if \( m_1 = -\frac{1}{2} \), then \( m_2 = \frac{-1}{-\frac{1}{2}} = 2 \).

Step3: Use y-intercept (if same)

The y - intercept \( b = 3 \) (from original line, assuming perpendicular line has same y - intercept here).

Step4: Write equation of perpendicular line

Using slope - intercept form \( y=mx + b \), with \( m = 2 \) and \( b = 3 \), we get \( y = 2x+3 \), which matches the given equation. Also, the original line has a negative slope (as it goes down from left to right).

Answer:

The slope of the original line is \( -\frac{1}{2} \), y - intercept \( b = 3 \), the line has a negative slope, and the equation of the perpendicular line is \( y = 2x + 3 \) (with the original line having negative slope, slope \( m=-\frac{1}{2} \), \( b = 3 \)).