Question

which equation represents a line that passes through $(4, \frac{1}{3})$ and has a slope of $\frac{3}{4}$?
$y-\frac{3}{4}=\frac{1}{3}(x-4)$
$y-\frac{1}{3}=\frac{3}{4}(x-4)$
$y-\frac{1}{3}=4(x-\frac{3}{4})$
$y-4=\frac{3}{4}(x-\frac{1}{3})$

Explanation:

Step1: Recall point-slope formula

The point-slope form of a line is $y - y_1 = m(x - x_1)$, where $m$ is the slope, and $(x_1, y_1)$ is a point on the line.

Step2: Identify given values

Given: $m = \frac{3}{4}$, $x_1 = 4$, $y_1 = \frac{1}{3}$

Step3: Substitute values into formula

Substitute into the point-slope form:
$y - \frac{1}{3} = \frac{3}{4}(x - 4)$

Step4: Match with options

Compare the derived equation to the provided choices.

Answer:

B. $y - \frac{1}{3} = \frac{3}{4}(x - 4)$