Question

9TH GRADE MATH HELPPPP

Answer 1

The equation in slope-intercept form is:

`y=(1)/(3)x+3`

So the second option is the correct one.

Explanation:

Step 1: Identify the gradient

The perpendicular line's equation is given as:

`y=-3x+4`

This equation is in the form of:

`y=mx+b`

Upon comparing the
`x` components of both equations, we get
`-3x=mx\\\text{Remove the}~ x~ \text{from both sides:}\\-3=m\\m=-3`

So, the gradient of this 'reference' equation is -3.

The equation we need to find is perpendicular to this 'reference' equation.

So, its gradient should be the negative reciprocal of the gradient of the 'reference' equation.

The negative reciprocal of -3 is:

`-(1)/((-3))\\=(1)/(3)`

So, the gradient of our equation is
`(1)/(3)`.

Step 2: Create the equation:

The equation crosses the x-axis at -9, which means its y-coordinate is 0 (at x-axis, y=0) ,so its coordinate is
`(-9,0)`.

The formula for an equation is:

`y-y_(1)=m(x-x_(1))`

The coordinate
`(x_(1),y_(1))` is
`(-9,0)`, and the gradient (
`m`) is
`(1)/(3)`.

Substitute the values into the equation:

`y-y_(1)=m(x-x_(1))\\y-0=(1)/(3)(x-(-9))\\\\\text{Simplify}\\y=(1)/(3)(x+9)`

`\text{Simplify further}\\y=(1)/(3)x+3`

Since, the slope-intercept form is:

`y=mx+b`

We already have our equation in the slope-intercept form.