Answer:
[tex]\boxed {\boxed {\sf y=\frac {1}{4}x-2}}[/tex]
Step-by-step explanation:
Since we are given a point and a slope, we can use the point-slope formula.
[tex]y-y_1=m(x-x_1)[/tex]
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:
Substitute these values into the formula.
[tex]y--1=\frac{1}{4}(x-4)[/tex]
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.
[tex]y--1=(\frac {1}{4}*x )+(\frac{1}{4} * -4)\\y+1= \frac {1}{4}x-1[/tex]
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.
[tex]y+1-1= \frac {1}{4}x-1-1[/tex]
[tex]y=\frac {1}{4}x-1-1\\y=\frac {1}{4}x-2[/tex]
The equation of the line is y=1/4x-2
