Answer: -2.5
Step-by-step explanation:
Given that the slope of the first line is [tex]M_{1}[/tex] and the slope of the second line is [tex]x_{2}[/tex] ,if the two lines are perpendicular then [tex]M_{1}[/tex][tex]x_{2}[/tex] = -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 [tex]\frac{1}{2}[/tex]. 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 - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
m = [tex]\frac{1}{2}[/tex]
[tex]x_{1}[/tex] = -1
[tex]y_{1}[/tex] = -3
substituting into the formula , we have
y - ( -3 ) = [tex]\frac{1}{2}[/tex]( x - {-1} )
y + 3 = [tex]\frac{1}{2}[/tex](x + 1)
y + 3 = [tex]\frac{1}{2}[/tex]x + [tex]\frac{1}{2}[/tex]
making y the subject of the formula in order to write the equation in slope - intercept form , we have
y = [tex]\frac{1}{2}[/tex]x + [tex]\frac{1}{2}[/tex] - 3
y = [tex]\frac{1}{2}[/tex]x - [tex]\frac{5}{2}[/tex]
Therefore , the y - intercept is - 2.5
