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=(5)/(3) \end{gathered}`

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

replacing:

`\begin{gathered} 1=2\cdot(5)/(3)+b \\ 1=(10)/(3)+b \\ b=1-(10)/(3) \\ b=-(7)/(3) \end{gathered}`

replacing, the equation in slope-intercept is

`y=(5)/(3)x-(7)/(3)`

The answer is the option B