Question

Rajah

Answer 1

The equation of a straight line AB is y = -2x - 11.

The x-intercept of the line is $-\frac{11}{2}$.

Solution:

Given data:

C(-2, 0) and D(0, -4)

Slope of CD:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-4-0}{0-(-2)}$

$m=\frac{-4}{2}$

m = -2

AB and CD are parallel lines.

If two lines are parallel then their slopes are equal.

Therefore slope of AB = -2

AB passes through the point (-3, -5).

Point-slope formula:

$y-y_1=m(x-x_1)$

Here, m = -2 and $x_1=-3, y_1=-5$

y - (-5) = -2(x - (-3))

y + 5 = -2(x + 3)

y + 5 = -2x - 6

Subtract 5 on both sides, we get

y = -2x - 11

The equation of a straight line AB is y = -2x - 11.

To find the x-intercept,substitute y = 0 in the equation of a line.

0 = -2x - 11

Add 11 on both sides.

11 = -2x

Divide by -2 on both sides.

$-\frac{11}{2}=x$

The x-intercept of the line is $-\frac{11}{2}$.