Question

Write an equation for line L in​ point-slope form and​ slope-intercept form.

L is parallel to y=4x.

Answer 1

Point-slope form is just one of many ways of describing a line which states that, given the slope of a line and a point on that line, you have enough information to completely describe that line.

A line is defined by some constant rate of change - its slope. If m is the slope of a line, then we can define m as


`m = (y-y_1)/(x-x_1)`

Where
`(x_1,y_1)` is some fixed point and
`(x,y)` is some other point on the line that we can vary. Here, we know that m = 4, and we're given a fixed point of
`(-1,3)` to work with, so we have


`4= (y-3)/(x-(-1))= (y-3)/(x+1)`

Multiplying both sides by
`x+1`, we get the equation in point-slope form:


`4(x+1)=y-3\\ y-3=4(x+1)`

To put the equation in slope-intercept form, we need to find the point where the line hits the y-axis. To do this, we can simply set x = 0:


`y-3=4(0+1)\\ y-3=4\\ y=7`

So, the line hits the y-axis at
`(0,7)`. Given our slope is 4, and given the general slope-intercept form of a line,


`y=mx+b`

Where m is our slope and b is our y-intercept, the slope-intercept form for our line would be


`y=4x+7`

Answer 2

Line L's slope intercept form is

y = 4x + 7

It's point slope form is

y - 3 = 4 (x - -1)

You can check the point slope form and match it with the slope intercept form:

y - 3 = 4 (x - -1)

y - 3 = 4x + 4

y = 4x + 7

y = 4x + 7 = y = 4x + 7