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To get a parallel graph, you need to have the same slope m as the original equation. So the new equation would be y=2x+b. Plug in the point to find a line that passes through it. \[4=2(3)+b\] Next you have to find b. \[4=6+b\] \[-2=b\] The final equation will be \[y=2x-2\]
A line that has a given slope, m, and passes through point (x1, y1) has the equation:
y = y1 = m(x - x1)
You are given a point, (3, 4) which is (x1, y1), so you have x1 = 3, and y1 = 4.
All you need is the slope of the parallel line.
Parallel lines have the same slope. So the slope you need is the same as the slope of
y = 2x - 7
y = 2x - 7 is written in the slope-intercept form, which is y = mx + b, where m = slope, and b = y-intercept
Just by looking at y = 2x - 7, you can see that the slope is m = 7.
Now use m = 7, x1 = 3, and y1 = 4 in the equation of a line above and find the equation of the line.