Question

Write the slope intercept form of the equation of the line.Help

Answer 1

Our final equation is
`\bold{y = (1)/(4)x + 3}.`

Explanation:

We are given a coordinate point and the slope of a line. We need to know that:

• The slope-intercept form of a line is
  `\text{y = mx + b},` where m is the slope of the line and b is the y-intercept of the line.
• The point-slope formula is y - y₁ = m(x - x₁).

We want to end up at the slope-intercept form of the equation. Therefore, we can use the point-slope formula and substitute our values and solve the equation.

`y - 2 = (1)/(4)(x - (-4))\\\\y - 2 = (1)/(4)x + 1\\\\\small\boxed{\bold{y = (1)/(4)x + 3}}`

Therefore, we have determined that our equation in slope-intercept form is
`\bold{y = (1)/(4)x + 3}`.

Answer 2

`\huge\boxed{y=(1)/(4)x+3}`

Hey! Let's start off with the point-slope form equation:

`y-y_1=m(x-x_1)`

In this equation,
`m` represents the slope and
`(x_1, y_1)` is the known point.

Substitute in the values we know:

`y-2=(1)/(4)(x-(-4))`

Subtracting a negative number is the same as adding a positive number.

`y-2=(1)/(4)(x+4)`

Distribute the
`(1)/(4)`:

`y-2=(1)/(4)x+1`

Add
`2` to both sides to get the equation in slope-intercept form, which is
`y=mx+b`:

`\boxed{y=(1)/(4)x+3}`