1. What is the equation of the line that passes through (4,-1) and (-2,3)?

Question

2. What is the equation of the line with an x-intercept of -1 and a y-intercept of 2?

Answer 1

1. The slope of that line is
m = (y2 - y1)/(x2 - x1) = 4/-6 = -2/3

Using y = mx + b standard format,
and the second data point valuesl
3 = (-2/3)*(-2) + b.
so b = 3 - 4/3 = 5/3

y = (-2/3)x +5/3
or
3y = 5 - 2x

2. When x=0, y = 2
When y = 0, x = -1

y = m x + 2
0 = m*(-1) +2
m = 2
y = 2x + 2

Answer 2

2nd question shortcut: or a straight line, use
x/(x-intercept) + y/(y-intercept) = 1

x/-1 + y/2 = 1
multiply each term by -2
2x - y = -2

done.