Write the linear equation that gives the rule for the table, where the x, y values are (0, 20), (1, 40), (2, 60), (3, 80). Write your answer as an equation with y first, followed b... Write the linear equation that gives the rule for the table, where the x, y values are (0, 20), (1, 40), (2, 60), (3, 80). Write your answer as an equation with y first, followed by an equals sign.
Understand the Problem
The question asks you to find the linear equation that represents the relationship between x and y as given in the table. The answer must be in the format y = (equation in terms of x).
Answer
$y = 20x + 20$
Answer for screen readers
$y = 20x + 20$
Steps to Solve
- Find the slope
The slope of a linear equation can be found using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Using the points $(0, 20)$ and $(1, 40)$ from the table: $m = \frac{40 - 20}{1 - 0} = \frac{20}{1} = 20$
- Find the y-intercept
The y-intercept is the value of $y$ when $x = 0$. From the table, when $x = 0$, $y = 20$. So the y-intercept, $b$, is 20.
- Write the equation in slope-intercept form
The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We found that $m = 20$ and $b = 20$. Therefore, the equation is: $y = 20x + 20$
$y = 20x + 20$
More Information
The equation represents a line that passes through all the points in the table. For every increase of 1 in $x$, $y$ increases by 20.
Tips
A common mistake is to miscalculate the slope or the y-intercept. Always double-check your calculations and make sure you are using the correct points from the table.
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