How do you write the point slope form of the equation given (-4,0) parallel to #y=3/4x-2#?

1 Answer
smendyka
Feb 22, 2017

#(y - color(red)(0)) = color(blue)(3/4)(x + color(red)(4))#

Explanation:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

#y = color(red)(3/4)x - color(blue)(2)#

Therefore the slope of this line is #color(red)(m = 3/4)#

Because the line we are looking for is parallel to the line in the problem we know it will have the same slope.

We can now use the point-slope formula to find the equation for the line we are looking for. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

Substituting the point from the problem and the slope from the parallel line gives:

#(y - color(red)(0)) = color(blue)(3/4)(x - color(red)(-4))#

#(y - color(red)(0)) = color(blue)(3/4)(x + color(red)(4))#

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