Question

Use point-slope form to write the equation of a line that passes through the point left bracket, minus, 14, comma, minus, 11, right bracket(−14,−11) with slope start fraction, 5, divided by, 3, end fraction

3
5
​
.

Answer 1

Left in point-slope form:
`y+11 = (5)/(3) *(x+14)`

Simplest form:
`y=(5)/(3)x+(37)/(3)`

Explanation:

Assuming your original point is (-14, -11) and your slope is
`(5)/(3)`.

The point slope form can be written as
`y-y_(1) = m*(x-x_(1) )`.

In this equation, x and y should be left alone, while
`x_(1)` and
`y_(1)` should be filled in from your original point. The slope is represented by m.

Substituting your point and slope into this equation:

`y-y_(1) = m*(x-x_(1) )\\y-(-11) = m*(x-(-14))\\y+11 = m*(x+14)\\y+11 = (5)/(3) *(x+14)`

If you need to get the equation to the simplest form:

`y+11 = (5)/(3) *(x+14)\\y = (5)/(3) *(x+14)-11\\y=(5)/(3)x+(70)/(3) -11\\y=(5)/(3)x+(70)/(3) -(33)/(3) \\y=(5)/(3)x+(37)/(3)`