y = -3x + 7 is an equation which gives us a line parallel to the line y = -3x + 1, or the line -3x - 1.
The equation given represents the slope-intercept form of the equation for a line. Slope-intercept takes the form y = mx + b. In this form the the value of m represents the slope of the line, while b represents the Y intercept. All lines with the same slope are parallel (unless they're exactly the same.) So to find a parallel line, we simply adjust the Y intercept to any value other than the one given.
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y = 3x + 1 is a linear equation - it is the equation for a graph of a straight line that crosses the y axis at 1 and the x axis at -1/3, and has a gradient (slope) of 3.
y = 3x - 3
put both equations in standard form y - 3x = -5 (equation 1) -7y + 21x = 35 (equation 2) multiply equation 1 by 7 (this is done so either one of your variables will cancel... if both variables cancel then these lines are parallel) 7y - 21x = -35 -7y + 21x = 35 0 = 0 therefore your lines are parallel
Substitute the point into the equation, eg. if you have point (1,2) and equation y=3x+7 you get 2=3*1+7 =10 2 doesnt equal 10, so (1,2) isn't on the graph y=3x+7
It can be many things however it must have the same slope of 3 and a different Y-Intercept. So it could be 3x+2, or 3x+ 3, 3x+4 and on and on