Question

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

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

$m = \frac{y-y_1}{x-x_1}$

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

$4= \frac{y-3}{x-(-1)}= \frac{y-3}{x+1}$

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