The required equation of line is:
[tex]y = \frac{1}{2}x[/tex]
Step-by-step explanation:
Given equation of line is:
y=-2x-3
The coefficient of x is the slope of line as the equation is in slope intercept form
Let m1 be the slope of given graph of line
So,
[tex]m_1=-2[/tex]
The product of slopes of perpendicular lines is -1
Let m2 be the slope of required line
Then
[tex]m_1.m_2 = -1\\-2 . m_2 = -1\\m_2 = \frac{-1}{-2}\\m_2 = \frac{1}{2}[/tex]
the slope-intercept form of line is:
[tex]y=m_2x+b[/tex]
Putting the value of slope
[tex]y=\frac{1}{2}x+b[/tex]
To find the value of b, putting the given point (-2,-1) in equation
[tex]-1=\frac{1}{2}(-2)+b\\-1 = -1 +b\\-1+1 = b\\b = 0[/tex]
Hence,
The required equation of line is:
[tex]y = \frac{1}{2}x[/tex]
Keywords: Equation of line, slope-intercept form
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