Write the linear equation that gives the rule for this table with the x and y values (4,0), (5,1), (6,2), (7,3). Write the answer as an equation with y first, followed by an equals... Write the linear equation that gives the rule for this table with the x and y values (4,0), (5,1), (6,2), (7,3). Write the 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 in the given table. The table provides pairs of x and y values. We need to determine a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept, that fits these pairs.
Answer
$y = x - 4$
Answer for screen readers
$y = x - 4$
Steps to Solve
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Calculate the slope ($m$) We can use the formula for the slope of a line given two points $(x_1, y_1)$ and $(x_2, y_2)$: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's use the points (4, 0) and (5, 1) from the table. $m = \frac{1 - 0}{5 - 4} = \frac{1}{1} = 1$.
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Use the slope-intercept form ($y = mx + b$) Now that we have the slope $m = 1$, we can plug it into the equation $y = mx + b$: $y = 1x + b$ which simplifies to $y = x + b$.
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Find the y-intercept ($b$) Plug in one of the points from the table into the equation to solve for $b$. Let's use the point (4, 0): $0 = 4 + b$. Subtract 4 from both sides: $b = -4$.
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Write the equation Now that we have $m = 1$ and $b = -4$, we can write the equation: $y = 1x - 4$, which simplifies to $y = x - 4$.
$y = x - 4$
More Information
The equation represents a line where for every increase of 1 in $x$, $y$ also increases by 1. The line intersects the y-axis at -4.
Tips
A common mistake is incorrectly calculating the slope by swapping the $x$ and $y$ values in the formula. Also, an arithmetic error while solving for the y-intercept is possible.
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