Question

Write the equation of the line for the following table of values.

x. -3 -5 -7 -9 -11


y. -16 -26 -36 -46 -56


Plz helppp 35 points:)​

Answer 1

We conclude that the equation of the line is:

• 
  `y = 5x + 1`

Explanation:

The slope-intercept form of the line equation

`y = mx+b`

where

• m is the slope

• b is the y-intercept

Given the data table

x -3 -5 -7 -9 -11

y -16 -26 -36 -46 -56

From the table taking two points

• (-3, -16)

• (-5, -26)

Determining the slope between (-3, -16) and (-5, -26)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-3,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-5,\:-26\right)`

`m=(-26-\left(-16\right))/(-5-\left(-3\right))`

`m=5`

Thus, the slope of the line is: m = 5

substituting m = 5 and (-3, -16) in the slope-intercept form of the line equation to determine the y-intercept b

`y = mx+b`

-16 = 5(-3) + b

-16 = -15 + b

b = -16+15

b = 1

Thus, the y-intercept b = 1

now substituting m = 5 and b = 1 in the slope-intercept form of the line equation

`y = mx+b`

`y = 5x + 1`

Therefore, we conclude that the equation of the line is:

• 
  `y = 5x + 1`