Slope-intercept form of the equation described.

Question

through: (-3,4), parallel to y=-4/3x+3

Answer 1

1. If the line is parallel to y=-4/3x+3, then it will have the same slope
2. Point slope form: y-y₁=m(x-x₁)
3. y-4=-4/3(x+3)
4. Slope intercept form: y=mx+b
5. y=-4/3x

Answer 2

through: (-3,4), parallel to y=-4/3x+3

We are searching for a parallel line. We get to keep the same slope as y=-4/3x+3. Isn't that exciting?

Slope of the new line: (-4/3).

We have the desired slope, and we need a point. We are asked for (-3,4). Plug these values into the point-slope formula. y-y₁-m(x-x₁). Plug -3 into x₁ and plug in 4 into y₁. We now get:

y-(4) = (-4/3)(x-(-3)), or simply:

y - 4 = (-4/3) (x + 3).

Simplify:

y - 4 = (-4/3)x - 4.

Add 4 to both sides:

y = (-4/3)x. This is a line with slope (-4/3) and y-intercept of (0,0), that is, the origin.