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 problem asks us to find the linear equation that represents the relationship between x and y as shown in the table. We need to determine the slope and y-intercept from the given data points and then express the equation in the form of y = mx + b, where m is the slope and b is the y-intercept. Finally, we will write the equation with y first, followed by an equals sign.
Answer
$y = 13x$
Answer for screen readers
$y = 13x$
Steps to Solve
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Calculate the slope (m) The slope $m$ is the change in $y$ divided by the change in $x$. We can use any two points from the table to calculate the slope. Let's use the points $(0, 0)$ and $(1, 13)$. $$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{13 - 0}{1 - 0} = \frac{13}{1} = 13 $$ So, the slope $m = 13$.
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Determine the y-intercept (b) The y-intercept is the value of $y$ when $x = 0$. From the table, we see that when $x = 0$, $y = 0$. Therefore, the y-intercept $b = 0$.
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Write the equation in slope-intercept form The slope-intercept form of a linear equation is $y = mx + b$. Substituting the values we found for $m$ and $b$, we get: $y = 13x + 0$, which simplifies to $y = 13x$.
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Write the equation with $y$ first The equation is already in the desired format: $y = 13x$.
$y = 13x$
More Information
The table represents a direct proportional relationship between $x$ and $y$, where $y$ is always 13 times $x$.
Tips
A common mistake is to incorrectly calculate the slope by swapping the values in the numerator or denominator. Another mistake is incorrectly identifying the y-intercept. Also not writing the equation with y first.
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