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

Solution:

Given, the points (-6, 10) and (12, -2).

We have to find the x-intercept of the line.

The equation of the line passing through two points is given by

\(\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{x-x_{1}}{x_{2}-x_{1}}\)

\(\frac{y-10}{-2-10}=\frac{x-(-6)}{12-(-6)}\)

\(\frac{y-10}{-12}=\frac{x+6}{18}\)

18(y - 10) = -12(x + 6)

18y - 180 = -12x - 72

12x + 18y = 180 - 72

12x + 18y = 108

Dividing by 6 on both sides,

2x + 3y = 18

Therefore, the equation of the line is 2x + 3y - 18 = 0.

X-intercept is where the line crosses the x-axis or where y = 0

So, put y = 0 in the given equation

2x + 3(0) = 18

2x = 18

x = 18/2

x = 9

Therefore, the x-intercept of the line is 9.

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

Summary:

The x-intercept of the line containing the points (-6, 10) and (12, -2) is 9.