Equation perpendicular to y=-2x+5 and goes through point (-3,4)


Answer:

y = \frac{1}{2} x + \frac{11}{2}

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + 5 ← is in slope- intercept form

with slope m = - 2

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{-2} = \frac{1}{2}, thus

y = \frac{1}{2} x + c ← is the partial equation

To find c substitute (- 3, 4) into the partial equation

4 = - \frac{3}{2} + c ⇒ c = 4 + \frac{3}{2} = \frac{11}{2}

y = \frac{1}{2} x + \frac{11}{2} ← equation of perpendicular line


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