Question 1063510
Write the slope-intercept form of the equation with the given characteristics.
1. Slope = 3/2, y - intercept is at (0,-4)

Use the equation y = mx + b where m is the slope and b is the y-intercept.
Given: m = 3/2 and b = -4
Hence the equation of the line is {{{highlight(y = (3/2)x - 4)}}}

2. Passes through (3,-1) and (4,-6)

First, compute the slope.
The slope is equal to "change in y" divided by "change in x"
slope, m = {{{((-6) - (-1))/(4-3) = -5}}}

Next, we use the point-slope form {{{y - y[1] = m(x - x[1])}}}
We choose ({{{x[1]}}}, {{{y[1]}}}) = (3, -1)
y - (-1) = -5(x - 3)
y + 1 = -5x + 15
{{{highlight(y = -5x + 14)}}}  is the equation of the line


3. Parallel to the line y = -4x + 2, and passes through (1,-3)
Use the fact that parallel lines have equal slopes.
{{{y - y[1] = m(x - x[1])}}}
y - (-3) = -4(x - 1)
y + 3 = -4x + 4
{{{highlight(y = -4x + 1)}}}