Find the rule of the mapping for the given pairs of (x, y) values: (0, 5), (2, 3), (4, 1), (6, −1), (8, −3).

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Identify the given points from the mapping. We have the following pairs of (x, y) values: (0, 5), (2, 3), (4, 1), (6, −1), (8, −3). Step 2: Calculate the slope (m) of the linear relationship. The slope is given by the formula m = (y₂ − y₁)/(x₂ − x₁). Using the first two points (0, 5) and (2, 3): m = (3 − 5)/(2 − 0) = (−2)/(2) = −1 Step 3: Determine the y-intercept (c). The y-intercept is the value of y when x = 0. From the table, when x = 0, y = 5. So, the y-intercept c = 5. Step 4: Write the rule of the mapping in the form y = mx + c. Substitute the calculated slope m = −1 and y-intercept c = 5 into the equation: y = −1x + 5; y = −x + 5; The rule of the mapping is y = −x + 5.

Find the rule of the mapping for the given pairs of (x, y) values: (0, 5), (2, 3), (4, 1), (6, -1), (8, -3).

Answer

Step-by-step solution

Identify the given points from the mapping.

Calculate the slope ( $m$ ) of the linear relationship.

Determine the y-intercept ( $c$ ).

Write the rule of the mapping in the form $y = mx + c$ .

Try one yourself

Still stuck on this one?

More Mathematics Questions