Question

Write the equation of a line that goes through the point (4,-7) and is parallel to a line with a slope of 1/10

Answer 1

The standard equation of a line is y = mx + b thus the final form of the resulting equation should be in this form. Parallel lines are lines with similar or equal slopes (same degree of inclination and direction) so the unknown equation of this line should have a slope of 1/10 as well. To use the point given, another equation form is to be used that is y-y1 = m(x-x1) where (x1,y1) is the point coordinate and m is the slope. Substituting, 
y + 7 = 1/10 *(x-4)
Simplifying,
y +7 = 1/10 x - 2/5
y = 1/10 x - 37/5
Multiplying the overall equation by 10, 
10 y = x - 74