Write an equation of the line that passes through (1,2) and is parallel to the line y=−5x+4.

Answer 1

Let's use slope intercept form y = mx + b where m = gradient, and b = y intercept.

y = -5x + 4 is already in this form (if not, rearrange). m = - 5 and b = 4

for two parallel lines, m1 = m2, hence we have an infinite number of parallel lines with form y = -5x + n.

for the specific parallel line through point (1,2) substitute the point values in the equation to get:

(2) = -5(1) + n => 2 = -5 + n => n = 7

hence required equation is y = -5x + 7

Answer 2

The key idea here is that parallel lines have the same slope. The equation you have is written in slope intercept form (y=mx+b) so you know that the slope is m=-5. Since you have a point (1,2) = (x1,y1) you have 2 options for finding your equation: first, you can plug m=-5, x=1, and y=2 into the slope-intercept equation y=mx+b to find b, or second, you can plug in for m, x1, and y1 in the point-slope equation y-y1=m(x-x1).