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 represents the relationship between x and y as shown in the given table. We need to determine the slope and y-intercept from the table data and express the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Answer
$y = 10x + 13$
Answer for screen readers
$y = 10x + 13$
Steps to Solve
- Calculate the slope (m)
The slope $m$ of a linear equation can be calculated using any two points from the table $(x_1, y_1)$ and $(x_2, y_2)$ using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Using the points (0, 13) and (2, 33): $$ m = \frac{33 - 13}{2 - 0} = \frac{20}{2} = 10 $$ So the slope $m$ is 10.
- Find the y-intercept (b)
The y-intercept is the value of $y$ when $x = 0$. From the table, when $x = 0$, $y = 13$. Therefore, the y-intercept $b$ is 13.
- Write the linear equation
The linear equation is in the form $y = mx + b$. We have $m = 10$ and $b = 13$. Substituting these values into the equation gives: $y = 10x + 13$.
$y = 10x + 13$
More Information
The equation $y = 10x + 13$ models the relationship between $x$ and $y$ in the given table. For every increase of 1 in $x$, $y$ increases by 10, starting from $y = 13$ when $x = 0$.
Tips
A common mistake is to incorrectly calculate the slope by swapping the numerator and denominator or using the wrong points from the table. Another mistake is misidentifying the y-intercept.
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