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

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.

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 = = = -

y = - 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 = - x + 6 ← equation of line

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

- 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

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