Write the linear equation that gives the rule for this table. Write your answer as an equation with y first, followed by an equals sign.
Understand the Problem
The question asks us to find the linear equation that describes the relationship between x and y as represented in the table. We need to determine the slope and y-intercept and then express the equation in the form y = mx + b.
Answer
$y = x + 18$
Answer for screen readers
$y = x + 18$
Steps to Solve
-
Calculate the slope (m) Choose two points from the table to calculate the slope. Let's use (2, 20) and (24, 42). The slope $m$ is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ $m = \frac{42 - 20}{24 - 2} = \frac{22}{22} = 1$
-
Find the y-intercept (b) Use the slope-intercept form of a linear equation, $y = mx + b$, and one of the points from the table to solve for b. Let's use the point (2, 20) and the slope $m = 1$: $20 = 1(2) + b$ $20 = 2 + b$ $b = 20 - 2 = 18$
-
Write the linear equation Now that we have the slope $m = 1$ and the y-intercept $b = 18$, we can write the linear equation in the form $y = mx + b$: $y = 1x + 18$ $y = x + 18$
$y = x + 18$
More Information
The equation $y = x+18$ describes the relationship between $x$ and $y$ in the given table. For every increase of 1 in $x$, $y$ also increases by 1, and when $x$ is 0, $y$ is 18.
Tips
A common mistake is incorrectly calculating the slope by swapping the x and y values in the formula. Another mistake is making an arithmetic error while solving for the y-intercept.
AI-generated content may contain errors. Please verify critical information
