Choose the equation below that represents the line passing through the point (1, -4) with a slope of .
Given a point (1,-4) and a known slope `m` . Find the equation of the line with slope `m` that goes through the point:
(1) Method 1: Every line has at least two points. Let another point on the line be (x,y). Then use the slope formula:
`m=(y-(-4))/(x-1)` or `m=(y+4)/(x-1)`
Multiply both sides by (x-1) to get `y+4=m(x-1)`
This is the equation in point-slope form. To convert to slope-intercept form clear the parantheses on the right and add 4 to both sides.
Ex: Suppose you are given m=-3. Then y+4=-3(x-1) or y=-3x+3-4 or y=-3x-1
(2) Method 2: You know the answer will be of the form y=mx+b. But you know a point on the line: (1,-4). Plug in these values for x and y respectively to find the value of b:
-4=m(1)+b so b=-4-m
Ex If m=-3 then -4=-3(1)+b ==> b=-4+3 or b=-1 Thus y=-3x-1 is the equation you seek.