Question

Find the equation of the line with the given slope and containing the given point: Slope -6/5 through (- 9,0)

Answer 1

`y=-(6)/(5) (x+9)`

Explanation:

Pre-Solving

We are given that a line passes through (-9,0) and has a slope of
`-(6)/(5)`.

There are 3 ways to write the equation of the line.

• Slope-intercept form, which is y=mx+b where m is the slope and b is the y-intercept.

• Standard form, which is ax+by=c, where a, b, and c are free integer coefficients but a and b cannot be 0.

• Point-slope form, which is
  `y-y_1=m(x-x_1)`, where m is the slope and
  `(x_1,y_1)` is a point.

As the question doesn't specify which form to put the answer in, any one of the forms can work. However, let's write the equation in point-slope form, as that is the easiest.

Solving

First, substitute
`-(6)/(5)` as m.

`y-y_1=-(6)/(5) (x-x_1)`

Now, substitute -9 as
`x_1` and 0 as
`y_1`.

`y-0=-(6)/(5) (x--9)`

Simplify:

`y=-(6)/(5) (x+9)`

Answer 2

From the given: Slope (m) = -6/5 and point (-9, 0), we will use the Slope-Intercept Form in making the equation.

`\text{ y = mx + b}`

The slope-intercept form is given a y=mx+b where m is the slope and b is the y-intercept at point (0,b).

Let's solve for the y-intercept (b) substituting the slope (m) = -6/5 and (x,y) = (-9,0).

Thus, we get,

`\text{ y =mx + b}`
`\text{ 0 = (}(-6)/(5))(-9)\text{ + b }\rightarrow\text{ b = -(}\frac{-6\text{ x -9}}{5})\text{ = }(-54)/(5)`

Let's now make the equation substituting the slope (m) = (-6/5) and y-intercept (b) = (-54/5). We get,

`\text{ y = (}(-6)/(5))x\text{ + (}(-54)/(5))`
`\text{ y = -}(6)/(5)x\text{ - }(54)/(5)`