Question

What is the x-intercept of the line containing the points (–6, 10) and (12, –2)? 4 5 6 9

Answer 1

bearing in mind that to get the x-intercept of any expression, we can simply set y = 0, and then solve for "x".

so let's check the slope of that line thus we can use its equation and set y = 0 then.

`\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{12}-\underset{x_1}{(-6)}}}\implies \cfrac{-12}{12+6}\implies -\cfrac{12}{18}\implies -\cfrac{2}{3}`

`\bf \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{-\cfrac{2}{3}}[x-\stackrel{x_1}{(-6)}] \\\\\\ y-10=-\cfrac{2}{3}(x+6)\implies \stackrel{setting~y=0}{0-10=-\cfrac{2}{3}(x+6)}\implies -10=-\cfrac{2}{3}x-4 \\\\\\ -6=-\cfrac{2x}{3}\implies -18=-2x\implies \cfrac{-18}{-2}=x\implies 9=x`

Answer 2

x- intercept = 9

Explanation:

Find the equation of the line in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, 10) and (x₂, y₂ ) = (12, - 2)

m =
`(-2-10)/(12+6)` =
`(-12)/(18)` = -
`(2)/(3)`

y = -
`(2)/(3)` x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation

Using (12, - 2), then

- 2 = - 8 + c ⇒ c = - 2 + 8 = 6

y = -
`(2)/(3)` x + 6 ← equation of line

To find the x- intercept let y = 0, that is

-
`(2)/(3)` x + 6 = 0

Multiply through by 3

- 2x + 18 = 0 ( subtract 18 from both sides )

- 2x = - 18 ( divide both sides by - 2 )

x = 9 ← y- intercept