Question

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

Answer 1

Answer:

x = 9 is the x-intercept.

Step-by-step explanation:

We have given the coordinates (-6,10) and (12,-2).

We have to find the  x-intercept of the line containing these points.

First we find the slope m by using these points.

We know that m = (y₂-y₁)/(x₂-x₁)

m = -2/3

The general form of the equation of line is :

y = mx + c

Where c is the y intercept.

Using the first coordinate to find c .

10 = (-2/3)(-6) +c

c = 6

So, the required equation is :

y = (-2/3)x+6

We have to find the x-intercept.

For this we put y=0

(-2/3)x+6 = 0

2/3 x = 6

x  = 6(3/2)

x = 9 is the x-intercept.

Answer 2

Answer:

x = 9

Step-by-step explanation:

Given that,

coordinate 1  = (-6,10)

coordinate 2 = (12,-2)

Step 1

Find the slope of line which contain above coordinates

Formula to use

$m=\frac{y2 - y1}{x2-x1}$

m = $\frac{-2-10}{12+6}$

m  = -2/3

Step 2

Find the equation of the line

Formula to use

y = mx + c

where m is the slope =  -2/3

           c is the y intercept

Using coordinate (-6,10)

Plug in the formula

10 = -2/3(-6) + c

10 = 4 + c

c = 10-4

c = 6

So, the equation will be

y = -2/3x + 6

Step 3

Find the x-intercept

we know that the x-intercept is the value of x when the value of y is equal to zero

so substitute y with 0 in the equation

when y = 0

0 = -2/3x + 6

2/3x = 6

x = 6(3/2)

x = 9