Final answer:
The equation of line b, which is parallel to Line A, is found by calculating its slope using the given points of Line A and then using the point it passes through to find the y-intercept. The final equation of Line b in slope-intercept form is y = -10x + 22.
Step-by-step explanation:
To find the equation of line b in slope-intercept form, we first need to determine the slope of Line A, as Line A is parallel to line b and thus they will have the same slope. Using the points (1, 9) and (2, -1) on Line A, we calculate the slope (m) by subtracting the y-coordinates and dividing by the subtraction of the x-coordinates: m = (-1 - 9) / (2 - 1) = -10. Since line b is parallel to Line A, its slope will also be -10.
Now that we know the slope of line b is -10, we can use the point (1, 12) through which Line b passes to find the y-intercept (b). The slope-intercept form of a line is given by y = mx + b. Substituting the known values, we have 12 = -10(1) + b. Solving for b gives us b = 12 + 10 = 22.
Therefore, the equation of Line b in slope-intercept form is y = -10x + 22.