Fill in the missing numbers to complete the linear equation that gives the rule for this table: x y 5 6 6 -1 7 -8 8 -15 y = x +
Understand the Problem
This question asks us to find the equation of a line given a table of values. In the given table we have x and y values. You need to find the slope and y-intercept, then sub those values into an equation of a line in slope intercept form, which is given by y = mx + b, where slope is m, and y intercept is b.
Answer
$y = -7x + 41$
Answer for screen readers
$y = -7x + 41$
Steps to Solve
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Calculate the slope The slope $m$ of a line can be found using two points $(x_1, y_1)$ and $(x_2, y_2)$ from the table with the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using the points (5, 6) and (6, -1): $$m = \frac{-1 - 6}{6 - 5} = \frac{-7}{1} = -7$$
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Use the slope-intercept form to find the y-intercept
The slope intercept form of a line is: $$y = mx + b$$ Where $m$ is the slope and $b$ is the y-intercept.
- Plug in values to find the $y$-intercept
Plug in the slope $m = -7$ and a point from the table (5, 6) into the slope-intercept form:
$$6 = -7(5) + b$$ $$6 = -35 + b$$ $$b = 6 + 35$$ $$b = 41$$
- Write the final equation Now that we have the slope $m = -7$ and the $y$-intercept $b = 41$, we can write the equation of the line: $$y = -7x + 41$$
$y = -7x + 41$
More Information
The equation of the line that represents the table of values is $y = -7x + 41$. This means for every increase of 1 in $x$, $y$ decreases by 7, and the line crosses the y-axis at $y = 41$.
Tips
A common mistake is to miscalculate the slope by subtracting the x values from the y values, or not keeping the signs (positive, negative) correct. Another mistake is making an error when solving for the y intercept ($b$). Always double check your calculations and make sure you are using the correct formula.
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