Question

Which equation represents a line that passes through (4, 5) and has a slope of ?

Oy--(-4)
Oy-- (-4)
Oy- } = 4(x-)
Oy- 4 = (x - 1)

Answer 1

`y - (1)/(3) = (3)/(4) (x - 4)`

Explanation:

Given the line passes through (4, 1/3) and it's slope is 3/4

`y = mx + c`

`slope = m`

`m = (3)/(4)`

`y = (3)/(4) x + c`

At (4, 1/3)

`(1)/(3) = (3)/(4) (4) + c`

`c = - (8)/(3)`

`y - intercept = - (8)/(3)`

The equation of the line:

`y = (3)/(4) x - (8)/(3)`

The answer is:

`y - (1)/(3) = (3)/(4) (x - 4)`

*if you expand the equation above you will get the equation of line you initially got*

Answer 2

B

Explanation:

Since we are given a point and the slope, we can use the point-slope form. Point-slope form is given by:

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

Where (x₁, y₁) is a point and m is our slope.

Let's let our point (4, 1/3) be (x₁, y₁) respectively.

We also know that our slope is 3/4. So, we will substitute 3/4 for m.

This yields:

`\displaystyle y-(1)/(3)=(3)/(4)(x-4)`

The choice that represents this is B.

So, our correct answer is B.

And we're done!