Answer:
[tex]y=-3x+5[/tex]
Step-by-step 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:
[tex]y=mx+b[/tex]
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:
[tex]\rightarrow y=mx+b\\\rightarrow(-1)=(-3)(2)+b[/tex]
Now, you can solve for b.
[tex]\rightarrow-1=(-3\times2)+b\\\rightarrow-1=-6+b\\\rightarrow5=b\\\rightarrow b = 5[/tex]
Finally, with both the slope and y-intercept, you can write the equation of the line:
[tex]y=-3x+5[/tex]
