The equation of a straight line AB is y = -2x - 11.
The x-intercept of the line is [tex]-\frac{11}{2}[/tex].
Solution:
Given data:
C(-2, 0) and D(0, -4)
Slope of CD:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$m=\frac{-4-0}{0-(-2)}[/tex]
[tex]$m=\frac{-4}{2}[/tex]
m = -2
AB and CD are parallel lines.
If two lines are parallel then their slopes are equal.
Therefore slope of AB = -2
AB passes through the point (-3, -5).
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Here, m = -2 and [tex]x_1=-3, y_1=-5[/tex]
y - (-5) = -2(x - (-3))
y + 5 = -2(x + 3)
y + 5 = -2x - 6
Subtract 5 on both sides, we get
y = -2x - 11
The equation of a straight line AB is y = -2x - 11.
To find the x-intercept,substitute y = 0 in the equation of a line.
0 = -2x - 11
Add 11 on both sides.
11 = -2x
Divide by -2 on both sides.
[tex]$-\frac{11}{2}=x[/tex]
The x-intercept of the line is [tex]-\frac{11}{2}[/tex].
