Question

Complete the slope-intercept form of the linear equation that represents the

relationship in the table.

Answer 1

`\mathsf{y=3x-4}`

Explanation:

`\mathsf{point \ slope \ form \ of \ linear \ equation: \ \ y-y_1=m(x-x_1)}`

`\mathsf{slope \ (m)=(y_2-y_1)/(x_2-x_1)}}`

(where m is the slope and
`\mathsf{(x_1,y_1)}` and
`\mathsf{(x_2,y_2)}` are points on the line)

Given:

• 
  `\mathsf{(x_1,y_1)=(1,-1)}`
• 
  `\mathsf{(x_2,y_2)=(4,8)}`

`\implies \mathsf{slope=(8--1)/(4-1)}=3}`

Substuting m = 3 and point (1, -1) into the point-slope form of a linear equation:

`\implies \mathsf{y-(-1)=3(x-1)}`

`\implies \mathsf{y=3x-4}`