Question

Find the equation of the line

With a slope of 2/3 that goes through the point (4, 5)

With a slope of (-1/3) that goes through the point (2, -4)

With a slope of 3 that goes through the point (-5, -1)

Answer 1

I would do the first one this way.
The equation for a straight line is
y = mx + b where m is the slope and b is the y intercept. If you want the line to go through (4,5) and slope = m = 2/3, then
set y = 5, m = 2/3, and x = 4
5=(2/3)*4 + b
Solve for b.
Multiply both sides by 3 to clear the fraction.
15 = 8 + 3b
3b = 7 and b = 7/3 so th equation is
y = (2/3)x + (7/3) or to get rid of the fractions, it would be
3y = 2x + 7
CHECK:
plug in 4 for x and 5 for y
3*5=2*4 + 7
15 = 8 + 7
15 = 15.
The others are done the same way.
Check my work.