Question

This table gives a few (x,y) pairs of a line in the coordinate plane.

x y
48 -30
61 -45
74 -60
What is the x-intercept of the line?

Answer 1

(22,0)

Explanation:

Answer 2

22

Explanation:

First, find the equation of the line in slope-intercept form, y = mx + b.

Using the coordinates of these two pairs, (48, -30) and (61, -45), the slope (m) can be calculated as follows:

`m = (y_2 - y_2)/(x_2 - x_1) = (-45 -(-30))/(61 - 48) = (-15)/(13)`

`slope (m) = -(15)/(13)`

Find the y-intercept (b) by substituting x = 48, y = -30, and
`m = -(15)/(13)` into y = mx + b:

`-30 = -(15)/(13)(48) + b`

Solve for b.

`-30 = -(720)/(13) + b`

Add
`-(720)/(13)` to both sides

`-30 + (720)/(13) = b`

`(-390 + 720)/(13) = b`

`(330)/(13) = b`

`b = (330)/(13)`

Substitute
`m = -(15)/(13)` and
`b = (330)/(13)` into y = mx + b

`y = -(15)/(13)x + (330)/(13)`

The x-intercept of the line with the above equation, would be the value of x when y = 0. This is the value of x where the line cuts across the x-axis. To calculate this, substitute y = 0 into
`y = -(15)/(13)x + (330)/(13)`.

`0 = -(15)/(13)x + (330)/(13)`

Subtract
`(330)/(13)` from both sides

`-(330)/(13) = -(15)/(13)x`

Divide both sides by
`-(13)/(15)x`

`(-(330)/(13))/(-(13)/(15)) = x`

`-(330)/(13)*-(13)/(15) = x`

`-(330)/(1)*-(1)/(15) = x`

`(330)/(15) = x`

`22 = x`

The x-intercept = 22