Answer:
[tex]y=3x-7[/tex]
Step-by-step explanation:
Parallel lines, by definition, never intersect. They have the same slope but different y-intercepts (otherwise they would be the same line) on a graph.
Slope-Intercept Form:
Slope-Intercept form is expressed as: [tex]y=mx+b[/tex], where
This form is super useful for linear equations as it gives us the two key features of a linear equation. It's how each of the options are formatted, so we know we'll have to use this form.
The line is parallel to [tex]y=3x-4[/tex], meaning it has a slope of 3, but also a y-intercept other than -4 (otherwise they would be the same equation).
So we can generally form an equation: [tex]y=3x+b\text{, }b\ne-4[/tex], so we can plug any value for "b" here (except -4) and have a parallel line
Since we not only want to find a parallel line, but also one that passes through a specific point, we can use our general parallel equation: [tex]y=3x+b\text{, }b\ne-4[/tex], and plug in known values. We of course already have the slope plugged in, but now we have a (x, y) coordinate, which we can plug in for x and y in the equation.
Original Equation:
[tex]y=3x+b[/tex]
Point given: (3, 2), substitute in x=3 and y=2:
[tex]2=3(3)+b[/tex]
Simplify:
[tex]2=9+b[/tex]
Subtract 9 from both sides:
[tex]-7=b[/tex]
Now we can take this value. and plug it back into the general equation:
[tex]y=3x+(-7)\implies y=3x-7[/tex]
Now we have our answer!
