Question

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

Answer 1

`(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))`