Question

a line goes through the points (-2, 4) and (6, 20). for numbers 6a - 6c, determine whether each statement is true or false.
6a. the line has a slope of 2. true false
6b. the equation of the line is y = 2x + 8. true false
6c. the point (2, 12) is on the line. true false

1. determine the equation for the linear function represented in the table below.

input x output y
-2 8
-1 5
2 -4
3 -7
4 -10
a. y = -3x + 2
b. y = -3x - 2
c. y = -3x
d. y = -2x - 3

Explanation:

6a

Step1: Recall slope formula

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

Step2: Substitute points \((-2,4)\) and \((6,20)\)

Here, \( x_1=-2,y_1 = 4,x_2=6,y_2=20 \). So \( m=\frac{20 - 4}{6-(-2)}=\frac{16}{8}=2 \).

Step1: Use point - slope form \( y - y_1=m(x - x_1) \)

We know \( m = 2 \) and use the point \((-2,4)\). So \( y-4=2(x + 2) \).

Step2: Simplify the equation

Expand: \( y-4=2x + 4 \), then \( y=2x+8 \).

Step1: Substitute \( x = 2 \) into \( y=2x + 8 \)

When \( x = 2 \), \( y=2\times2+8=4 + 8=12 \).

Step2: Check the point

The point \((2,12)\) gives \( y = 12 \) when \( x = 2 \) in the line equation, so it is on the line.

Answer:

TRUE

6b