Question

Identify the equation in slope-intercept form for the line containing the point (2,1) and parallel to y=5/3 x-1/3. Answers A. y=5/3x-1/3. B. y=5/3x-7/3. C. y=5/3 x -2/3. D. y=2/3x-1/3

Answer 1

We have the following:

the equation in slope-intercept form is

$y=mx+b$

where m is the slope and b is y-intercept

when two lines are parallel, the slope is the same

$\begin{gathered} m_1=m_2 \\ m=\frac{5}{3} \end{gathered}$

for b, x = 2 and y = 1, m = 5/3

replacing:

$\begin{gathered} 1=2\cdot\frac{5}{3}+b \\ 1=\frac{10}{3}+b \\ b=1-\frac{10}{3} \\ b=-\frac{7}{3} \end{gathered}$

replacing, the equation in slope-intercept is

$y=\frac{5}{3}x-\frac{7}{3}$

The answer is the option B