Find an equation of the line

Question

Find an equation of the line that  has the same y-intercept as the line y -8 x + 3 = 0 and  is parallel to the line 9 x -5 y = -11

Answer 1

So for the first equation, you need the y-intercept (in other words, the "b" in the equation Y = mX + b). We now put this equation in that form:

y-8x+3=0 (subtract 3 on both sides)

y-8x=-3 (add 8x to both sides)

y = 8x -3

As you can see it is in the form of y=mx+b, which means b = -3.

 

From the second equation, we need to ensure that this new equation is parallel to the line 9x-5y=-11. Parallel and perpendicular refers to the slope of a line. If two lines are parallel, then they have the same slope. If two lines are perpendicular, their slopes are reciprocals and opposite signs (i.e m=3 and m= -1/3). With this information, we need to find the slope of the second equation:

9x-5y= -11 (subtract both sides by 9x)

-5y = -9x - 11 (divide both sides by negative 5)

y = (9/5)x + 11/5

Note that two negatives equal a positive (that's why the sign changes when you divide everything by -5)

So now we see that the new equation needs to have a slope of (9/5). Thus our final equation is:

y= (9/5)x -3

 

Hope that helps!