Question

value: 3
find the slope between the two points. then identify the line that has perpendicular slope.
(-2,3)
(4,1)

a. $y = -\frac{1}{3}x + 3$
b. $y = 3x - 2$
c. $y = -0.5x + 3$
d. $y = -x+\frac{1}{3}$

Explanation:

1. First, find the slope between the two - points \((x_1,y_1)=(-2,3)\) and \((x_2,y_2)=(4,1)\):

• The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
• Substitute the values: \(m=\frac{1 - 3}{4-(-2)}=\frac{-2}{6}=-\frac{1}{3}\).

1. Then, find the slope of the perpendicular line:

• The slope of a line perpendicular to a line with slope \(m\) is the negative - reciprocal of \(m\).
• The negative - reciprocal of \(-\frac{1}{3}\) is \(3\).

1. Now, identify the line with the perpendicular slope:

• The equation of a line is in the form \(y = mx + b\), where \(m\) is the slope.
• For the line \(y = 3x-2\), the slope \(m = 3\).

Answer:

Slope between the two points: \(-\frac{1}{3}\); Line with perpendicular slope: b. \(y = 3x - 2\)