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a. The equation that relates Ann's age (x) and Tom's age (y) is a line
The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
From the table, the line passes through the points (4, 8) and (8, 12), then its slope is:
Substituting with m = 1 and the point (4, 8) into the general equation, we get:
8 = 1(4) + b
8 = 4 + b
8 - 4 = b
4 = b
Finally, the equation that compares Tom's and Ann's age is:
y = x + 4
b. To graph the line y = x + 4, we need to draw two points and then connect them with a line. Replacing with x = 0 into the equation:
y = 0 + 4
y = 4
then, the point (0, 4) is on the line. And we can also use the point (4,8)
