Question

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

Answer 1

Answer:

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

Step-by-step 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 $m=\dfrac{3}{4}$

point $\left9,\ \dfrac{1}{3}\right)\to x_1=4,\ y_1=\dfrac{1}{3}$

Substitute:

$y-\dfrac{1}{3}=\dfrac{3}{4}(x-4)$

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

$y-\dfrac{1}{3}=\dfrac{3}{4}x-3$            add 1/3 to both sides

$y=\dfrac{3}{4}x-2\dfrac{2}{3}$