Given the equation:
[tex]y=-\frac{4}{3}x+2[/tex]
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:
[tex]m=-\frac{4}{3}[/tex]
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
[tex]\begin{gathered} y=mx+b \\ \\ 1=-\frac{4}{3}\ast3+b \end{gathered}[/tex]
Let's solve for b which is the y-intercept.
We have:
[tex]\begin{gathered} 1=-\frac{4}{3}\ast3+b \\ \\ 1=-4+b \\ \\ \text{Add 4 to both sides:} \\ 1+4=-4+4+b \\ \\ 5=b \\ \\ b=5 \end{gathered}[/tex]
The y-intercept of the parallel line is: y = 5
Therefore, the equation of the line parallel to the given line is:
[tex]y=-\frac{4}{3}x+5[/tex]
ANSWER:
[tex]y=-\frac{4}{3}x+5[/tex]
