Question

Find the equation of the line that is parallel to the given line y= -4/3x+2 and passes through the point (3,1)Step By Step explanation please

Answer 1

Given the equation:

`y=-(4)/(3)x+2`

Let's find the equation of the line that is paralle to the given line that passes through (3, 1).

Apply the slope intercept form of a linear equation:

y = mx + b

Where:

m is the slope and b is the y-intercept.

Parallel lines have equal slopes.

Hence, the slope of the line parallel to the given line is:

`m=-(4)/(3)`

Now, to find the y-intercept(b) of the parallel line, input the point(3, 1) for the values of x and y, and solve for b.

Thus, we have:

Substitute 3 for x, 1 for y, and -4/3 for m

`\begin{gathered} y=mx+b \\ \\ 1=-(4)/(3)\ast3+b \end{gathered}`

Let's solve for b which is the y-intercept.

We have:

`\begin{gathered} 1=-(4)/(3)\ast3+b \\ \\ 1=-4+b \\ \\ \text{Add 4 to both sides:} \\ 1+4=-4+4+b \\ \\ 5=b \\ \\ b=5 \end{gathered}`

The y-intercept of the parallel line is: y = 5

Therefore, the equation of the line parallel to the given line is:

`y=-(4)/(3)x+5`

ANSWER:

`y=-(4)/(3)x+5`