Graph the line that passes through the given point and has the given slope. $( 3,2 ) , m = \frac { 5 } { 3 }$

Question

Quizplus · Accepted Answer

Using point-slope formula, we have:
$$y - y_1 = m(x - x_1)$$
Substituting the values given in the question, we get:
$$y - 2 = \frac{5}{3}(x - 3)$$
Simplifying, we get:
$$3y - 6 = 5x - 15$$
$$5x - 3y = 9$$
This is in the form of the equation of a line. Converting it into slope-intercept form, we get:
$$y = \frac{5}{3}x - 3$$
This is the equation of the line that passes through point $(3,2)$ and has a slope of $\frac{5}{3}$. Looking at the answer choices, we can see that the graph in option C matches this equation.

Graph the Line That Passes Through the Given Point and Has