Question

Fill in the missing numbers to complete the linear equation that gives the rules for this table.x: 3, 4, 5, 6y: 2, 3, 4, 5y = ?x - ?

Answer 1

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 a 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 (3, 2) and (4, 3), then its slope is:

$m=\frac{3-2}{4-3}=-1$

Replacing whit m = -1 and the point (3, 2) into the equation, we get:

2 = (-1)(3) + b

2 = -3 + b

2 + 3 = b

5 = b

Finally, the equation is:

y = -x + 5