The equation that represents the new path is: [tex]y = \frac{1}{4}x-7[/tex]
Step-by-step explanation:
Given path is:
[tex]y=-4x+10[/tex]
We have to find the equation of a path that will be perpendicular to given path and will pass through point (4,-6)
So first of all we have to find the slope of given line
As the equation of path is in slope-intercept form, the coefficient of x will be the slope of the path
so
m = -4
As the product of slopes of two perpendicular lines is -1
Let m1 be the slope of required line
[tex]m.m_1 = -1\\-4 . m_1 = -1\\m_1 = \frac{-1}{-4}\\m_1 = \frac{1}{4}[/tex]
The slope-intercept form is:
[tex]y=m_1x+b[/tex]
Putting the value of m1
[tex]y = \frac{1}{4}x+b[/tex]
Putting the point (4,-6) in the equation
[tex]-6 = \frac{1}{4}(4) +b\\-6 = 1+b\\b = -6-1\\b = -7[/tex]
Putting the value of b
[tex]y = \frac{1}{4}x-7[/tex]
So,
The equation that represents the new path is: [tex]y = \frac{1}{4}x-7[/tex]
Keywords: Equation of line, slope
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