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 to determine the linear equation represented by the table of x and y values. We need to find an equation in the form y = mx + b, where m is the slope and b is the y-intercept, from the give table..
Answer
$y = x - 1$
Answer for screen readers
$y = x - 1$
Steps to Solve
- Calculate the slope ($m$)
The slope $m$ of a linear equation can be found using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Using the points $(5, 4)$ and $(6, 5)$ from the table: $m = \frac{5 - 4}{6 - 5} = \frac{1}{1} = 1$
- Determine the y-intercept ($b$)
The equation of a line is $y = mx + b$. We know $m = 1$. We can use any point from the table to solve for $b$. Let's use the point $(5, 4)$. $4 = 1(5) + b$ $4 = 5 + b$ $b = 4 - 5$ $b = -1$
- Write the equation
Now that we have the slope $m = 1$ and the y-intercept $b = -1$, we can write the equation: $y = 1x - 1$ or $y = x - 1$
$y = x - 1$
More Information
The equation $y = x - 1$ describes the relationship between $x$ and $y$ in the given table. For every increase of 1 in $x$, $y$ also increases by 1. The y-intercept is -1, meaning the line crosses the y-axis at $y = -1$.
Tips
A common mistake is to incorrectly calculate the slope, or to mix up the x and y values when calculating it. Another common mistake is to incorrectly solve for b.
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