Given equation of the parallel line:
3x - 2y = 16
The line passes through the point: (-1, 1)
Parallel lines have the same slope.
Let's rewrite the equation of the parallel line in slope intercetpt form:
y = mx + b
Where m is the slope and b is the y-intercept.
We have:
[tex]\begin{gathered} 3x-2y=16 \\ \\ \text{Subtract 3x from both sides:} \\ -3x+3x-2y=-3x+16 \\ \\ -2y=-3x+16 \\ \\ \text{Divide all terms by -2:} \\ \frac{-2y}{-2}=\frac{-3x}{-2}+\frac{16}{2} \\ \\ y=\frac{3}{2}x+8 \end{gathered}[/tex]
The slope is 3/2
Substitute 3/2 for m in the slope intercept form.
[tex]y=\frac{3}{2}x+b[/tex]
To solve for the y-intercept, b, since the line passes through (-1, 1), substitute -1 for x and 1 for y:
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ \\ 1=\frac{3}{2}(-1)+b \\ \\ 1=-\frac{3}{2}+b \\ \\ \text{Multiply all terms by 2:} \\ 1(2)=-\frac{3}{2}\ast2+2(b) \\ \\ 2=-3+2b \\ \\ \text{Add 3 to both sides:} \\ 3+2=-3+3+2b \\ \\ 5=2b \\ \\ \text{Divide both sides by 2:} \\ \frac{5}{2}=\frac{2b}{2} \\ \\ \frac{5}{2}=b \\ \\ b=\frac{5}{2} \end{gathered}[/tex]
The y-intercept, b is 5/2
Therefore, the equation that represents the line is:
[tex]y=\frac{3}{2}x+\frac{5}{2}[/tex]
ANSWER:
[tex]y=\frac{3}{2}x+\frac{5}{2}[/tex]
