Can someone help me find the equations of the lines parallel to and perpendicular to the line y+4x=7, and through the point (1, 25).

Question

y+4x=7 through the point (1,25).

Answer 1

Parallel lines have the same slope. You want it to be in the form y=mx +b to find the slope easier.  So then take the given equation y+4x=7 and subtract 4x to both sides to get y by itself. When you do that you'll get y=7-4x and then to get in slope intercept form switch places of 7 and -4x, you'll get y=-4x+7 . Since the number in front of x is the slope, then the slope is -4. And that means the slope of the other line must also be -4. Now you then use point slope form y-y1=m(x-X1). m=-4 and the point is (x1,y1) so x1=1 and y1=25 so the final answer after replacing those values the answer is: y-25=-4(x-1). The slope perpendicular to this line is 1/4. Here is why:  because -4 as a fraction is -4/1. You flip the fraction --> -1/4 and change the sign----> 1/4. Then the equation of the line would be y-25=1/4(x-1) bc the only thing that changes is m value which is now 1/4.