What is the standard form of the equation of the line with a slope of two-thirds passing through the points negative 5 and nine?

Answer 1

With a slope of 2/3, the slope-intercept form of the equation is:

y = (2/3)x + b where b is the y-intercept.

If it passes through the point (-5, 9) -- I assume that's what you meant in the question -- then you substitute x=-5 and y=9:

9 = (2/3)(-5) + b and solve for b:

9 = -10/3 + b

b = 9 + 10/3 = 27/3 + 10/3 = 37/3

So now you have y = (2/3)x + 37/3

Multiply both sides by 3:

3y = 2x + 37

Rearrange:

2x - 3y + 37 = 0

which is standard form ax + by + c = 0