
Jonathan D. answered 09/08/19
Experienced Tutor - Psychology, Math, French
For 2 lines to be parallel, their slopes must be the same. In this problem, the equation is in Standard Form:
Ax+By=C
The slope of a line in standard form is -A/B, though if you forget that shortcut, you can always turn it into slope-intercept form. In this case, you could add the y over to the right side and 7 over to the left. The slope of this line is 7, so the slope of the new line must be 7, as well.
The problem provides a point that must be on the new line: (0,0). One way to obtain the new function is to use point-slope form which, as its name states, just requires the slope and a point on the line:
y-y1=m(x-x1), with (x1, y1) being the point on the line and (x,y) representing the variables.
If you substitute in our slope of m=7 and our point x1=0, y1=0:
y-0=7(x-0)
y=7x
Alternatively, if you think of the equation in slope-intercept form after getting the slope:
y=7x+b
the problem outright gives you the y-intercept (b), the point at which the line crosses the y-axis (the y value when x=0), which is 0, so you could also produce the equation more quickly by recognizing that.