Question

What is the y-intercept of the line perpendicular to 2x + y + 5 = 0 at (-1 , -3)?

Answer 1

Answer: -2.5

Step-by-step explanation:

Given that the slope of the first line is $M_{1}$ and the slope of the second line is $x_{2}$ ,if the two lines are perpendicular then $M_{1}$$x_{2}$ = -1 ,

The line given is 2x + y + 5 =0 , to find the slope of the line , we will need to make y the subject of the formula

2x + y +5 = 0

y = -2x -5

comparing the solution to the equation of line in slope - intercept form , which is given as y = mx + c , where m is the slope and c is the y-intercept. This means that the slope of the given line is -2.

Therefore , the slope of the line perpendicular to this line is given as $\frac{1}{2}$. The point given is (-1 , -3 ). Thus , to find the equation of the new line , we will use the formula for finding equation of line in slope-point form , which is given as :

y - $y_{1}$ = m ( x - $x_{1}$ )

m = $\frac{1}{2}$

$x_{1}$ = -1

$y_{1}$ = -3

substituting into the formula , we have

y - ( -3 ) = $\frac{1}{2}$( x - {-1} )

y + 3 = $\frac{1}{2}$(x + 1)

y + 3 = $\frac{1}{2}$x + $\frac{1}{2}$

making y the subject of the formula in order to write the equation in slope - intercept form , we have

y = $\frac{1}{2}$x + $\frac{1}{2}$ - 3

y = $\frac{1}{2}$x - $\frac{5}{2}$

Therefore , the y - intercept is - 2.5