Answer: y-intercept is -6
Step-by-step explanation: Calculate the slope of the line between the two given points:
Rise/Run = slope, m in the standard form of a straight line: y=mx+b, with b the y-intercept (the value of y when x=0).
Rise = 1 - (-6) = 7
Run = 4 - (-3) = 7
Slope = Rise/Run, 7/7, or 1
y=mx+b
y = 1x+ b
Find b by entering one of the two given points. I'll pick (4,1).
y = 1x+ b
What's important now is the next step. The equation "that is parallel" must have the same slope as the reference equation, 1 in this case.
[If, out of curiosity, you want the full equation of the reference line, we can find b in this way:
Enter one of the two given points and solve for b. I'll pick (4,1):
y = 1x+ b
1 = 1*(4)+ b
b = -3
y = 1x - 3 is the first equation.]
All we really needed from the first, or reference, equation is the slope, 1 in this case. Parallel lines have the same slope, so we want an equation in the form:
y=1x+b
This equation will be parallel, regardless of the value of b. But we want it to go through a specific point, (7,1). So use that point and solve for b:
y=1x+b
1=1*7+b
b=-6
The equation is y=1x-6