Question

Write an equation of the line (2,-1) and parallel to the line y=-3x+8

An equation of the parallel line is y= ?

Answer 1

`y=-3x+5`

Explanation:

A line being parallel to another means it has the same slope, so the slope of the new line is also -3.

Slope-intercept form is:

`y=mx+b`

where m is the slope, b is the y-intercept, and (x, y) is any point on the line. There are 4 variables in this equation, and we're already given 3 of them (slope, x, and y), so we can solve for the 1 unknown variable (y-intercept).

Plug in all known values:

`\rightarrow y=mx+b\\\rightarrow(-1)=(-3)(2)+b`

Now, you can solve for b.

`\rightarrow-1=(-3*2)+b\\\rightarrow-1=-6+b\\\rightarrow5=b\\\rightarrow b = 5`

Finally, with both the slope and y-intercept, you can write the equation of the line:

`y=-3x+5`