Write the equation of a line that is parallel to the line 3x + y = 4 and goes through the point (-2,1)

Question

I get the answer y= 3x -2 which is wrong. Can someone break down the solution to this? I'm following methods that are all over the internet but this particular equation is difficult to me.

Answer 1

The equation for the line 3x + y = 4 is in Standard Format (Ax+By=C).

You may, once and forever, convert this to slope-intercept form (y=mx+b) and find that the slope,

m, is (-A/B).

This and all parallel equations have a slope of -3.

The equation of the desired line (in Standard Format) is: 3x + y = C. The point (-2,1) is on that line and allows us to calculate the value of C.

3(-2) + 1 = C

C = -5

In Standard Form, the equation of the parallel line is: 3x + y = -5

Answer 2

Solving for y in the first equations gives you y= -3x +4 so the slope is -3. Using y=my+b I put in the point and the slope and solve for b

1= -3(-2)+b. 1=6+b then b= -5

last step write out y=my+b using our slope and b y= -3x - 5