Question

Which equation represents a line that passes though (4, 1/3) and has a slope of 3/4

Answer 1

`\large\boxed{y-(1)/(3)=(3)/(4)(x-4)\leftarrow\text{point-slope form}}\\\boxed{y=(3)/(4)x-2(2)/(3)\leftarrow\text{slope-intercept form}}`

Explanation:

The point-slope form of an equation of a line:

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

m - slope

(x₁, y₁) - point

We have

slope
`m=(3)/(4)`

point
`\left9,\ (1)/(3)\right)\to x_1=4,\ y_1=(1)/(3)`

Substitute:

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

Convert to the slope-intercept form (y = mx + b):

`y-(1)/(3)=(3)/(4)x-3` add 1/3 to both sides

`y=(3)/(4)x-2(2)/(3)`