You can identify the slope (m) of a line with the equation written in the form y=mx+b
Dashed line:
[tex]-6x+7y=-14[/tex]
Write the equation in the form y=mx+b (solve y):
[tex]\begin{gathered} 7y=6x-14 \\ y=\frac{6}{7}x-\frac{14}{7} \\ \\ y=\frac{6}{7}x-2 \end{gathered}[/tex]
The slope of the dashed line is: 6/7
[tex]m=\frac{6}{7}[/tex]
Two parallel lines have the same slope.
Then, the slope of any line parallel to the dashed line is: 6/7
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Find the equation of a parallel line that passes through (1,1)
The parallel line needs to have slope (m=6/7)
Uses the given point and the slope to find the y-intercept (b) in the equation y=mx+b:
[tex]\begin{gathered} y=mx+b \\ 1=\frac{6}{7}(1)+b \\ \\ 1=\frac{6}{7}+b \\ \\ 1-\frac{6}{7}=b \\ \\ \frac{7-6}{7}=b \\ \\ \frac{1}{7}=b \\ \\ \\ b=\frac{1}{7} \end{gathered}[/tex]
Then, the equation of a parallel line that passes through (1,1) is:
[tex]y=\frac{6}{7}x+\frac{1}{7}[/tex]
