Answer:
Step-by-step explanation:
As we go from (–2, 2) to (3, 4), x increases by 5 and y increases by 4. Thus, the slope of the line through (–2, 2) and (3, 4) is
m = rise / run = 4/5.
Use the slope-intercept form of the equation of a straight line:
y = mx + b becomes 4 = (4/5)(3) + b. Multiplying all three terms by 5, we eliminate the fraction: 20 = 12 + b. Thus, b = 8, and the equation of the line through (–2, 2) and (3, 4) is y = (4/5)x + 8.
A line parallel to this one would have the form y = (4/5)x + b; note that the slopes of these two lines are the same, but the y-intercept, b, would be different if the two lines do not coincide.
Unfortunately, you have not shared the ordered pairs given in this problem statement.
You could arbitrarily let b = 0. Then the parallel line has equation
y = (4/5)x; if x = 3, then y = (4/5)(3) = 12/5, and so (3, 12/5) lies on the parallel line.
