Question

Write an equation of the line shown. Then use the equation to find the value of x when y=112

Answer 1

`y = 8x + 16`

`x = 12`

Explanation:

Given two points on the line (0, 16) and (3, 40), an equation for the line can be written using the slope-intercept line equation which takes the format
`y = mx + b`.

Where,

`m = slope = (y_2 - y_1)/(x_2 - x_1)`

b = y-intercept or the point at which the line cuts the y-axis.

Let's find slope (m) using the slope formula:

Let,

`(0, 16) = (x_1, y_1)`

`(3, 40) = (x_2, y_2)`

`slope (m) = (40 - 16)/(3 - 0)`

`slope (m) = (24)/(3)`

`slope (m) = 8`

Find b. Substitute the values of x = 0, y = 16, and m = 8 in the slope-intercept formula to find b.

`y = mx + b`

`16 = 8(0) + b`

`16 = 0 + b`

`16 = b`

`b = 16`

Plug in the values of m and b into the slope-intercept formula to get the equation of the line.

`y = mx + b`

`y = 8x + 16`

Let's use the equation to find x when y = 112.

`y = 8x + 16`

Substitute y = 112 in the equation

`112 = 8x + 16`

`112 - 16 = 8x`

`96 = 8x`

Divide both sides by 8

`12 = x`

`x = 12`