Question

Write the slope intercept form of the line that travels through (4,-1) and is parallel to y=1/4x

Answer 1

`\boxed {\boxed {\sf y=\frac {1}{4}x-2}}`

Explanation:

Since we are given a point and a slope, we can use the point-slope formula.

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

where m is the slope and (x₁ , y₁) is the point the line passes through.

We know the point is (4, -1).

We have to find the slope. We know that the line is parallel to y=1/4x.

This line has a slope of 1/4 (1/4 is the coefficient of x), and parallel lines have the same slope. Therefore, the line we are finding also has a slope of 1/4.

So, we know that:

• m=1/4
• x₁= 4
• y₁= -1

Substitute these values into the formula.

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

Now we must put the equation into slope-intercept form, or y=mx+b. We have to isolate y on one side of the equation.

First, distribute the 1/4. Multiply each term inside the parentheses by 1/4.

`y--1=(\frac {1}{4}*x )+((1)/(4) * -4)\\y+1= \frac {1}{4}x-1`

1 is being added to y. The inverse of addition is subtraction, so subtract 1 from both sides of the equation. This will leave the variable y by itself.

`y+1-1= \frac {1}{4}x-1-1`

`y=\frac {1}{4}x-1-1\\y=\frac {1}{4}x-2`

The equation of the line is y=1/4x-2