line j passes through the coordinate points (4,1) and (-3,_6).what is the y-intercept of the equation that is parallel; to line j and passes through the point,(7,1)

 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