Question

A. Write an equation that compares Tom sand Ann's ages.b. Draw a graph to represent theequation

Answer 1

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

From the table, the line passes through the points (4, 8) and (8, 12), then its slope is:

$m=\frac{12-8}{8-4}=\frac{4}{4}=1$

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)