Respuesta :
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.
[tex]\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}[/tex]
[tex]\bf \begin{array}{|c|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[/tex]
Answer:
x- intercept = 9
Step-by-step 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 = [tex]\frac{-2-10}{12+6}[/tex] = [tex]\frac{-12}{18}[/tex] = - [tex]\frac{2}{3}[/tex]
y = - [tex]\frac{2}{3}[/tex] 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 = - [tex]\frac{2}{3}[/tex] x + 6 ← equation of line
To find the x- intercept let y = 0, that is
- [tex]\frac{2}{3}[/tex] 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
