Answer:
y=−35x−2
Explanation:
For parallel lines, the slope is the same. Since this given line is already given in the form y=mx+b, we know that the slope of any parallel line will also be m. Here, m=−35 from y=−35x+2.
The question is asking us to find an equation of the line that passes through the point (0,−2). Well, this means that our line will have a point where x=0 and y=−2, but with a given slope of m=−35. We just need to find a b such that the point (0,−2) exists on that line.
We can do this in two ways.
1) Use y=mx+b with x=0, y=−2, and m=−35 to solve b and find this general equation of the parallel line.
Let's plug in our values.
−2=(−35)(0)+b
b=−2
We now know our b, which we can plug into the new y=mx+b (of which we already know m, since it remains the same). So, the equation of the line parallel to y=−35x+2 that goes through the point (0,−2) is
y=−35x−2
OR
2) Use the point-slope form of y−y1=m(x−x1), where y1 and x1=coordinates of point on line and m=slope, to find the equation directly. Here, x1=0 and y1=−2, from (0,−2) and m is still −35.
Let's solve to find the equation of the line.
y−y1=m(x−x1)
y−(−2)=−35(x−0)
y+2=−35x
y=−35x−2
