Fill in the missing numbers to complete the linear equation that gives the rule for this table.
Understand the Problem
The question asks to fill in the missing numbers in the linear equation y = _x + _ that represents the relationship between x and y in the given table. The 'x' values range from 5 to 8, while the corresponding 'y' values range from 30 to 48. We need to determine the slope (coefficient of x) and the y-intercept to complete the equation.
Answer
$y = 6x + 0$
Answer for screen readers
$y = 6x + 0$
Steps to Solve
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Find the slope (m) The slope of a linear equation 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, 30) and (6, 36): $m = \frac{36 - 30}{6 - 5} = \frac{6}{1} = 6$ So, the slope is 6.
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Find the y-intercept (b) Now that we have the slope $m = 6$, we can use the slope-intercept form of a linear equation $y = mx + b$ and one of the points from the table to solve for $b$. Let's use the point (5, 30): $30 = 6(5) + b$ $30 = 30 + b$ $b = 30 - 30$ $b = 0$ So, the y-intercept is 0.
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Write the complete equation Now that we have the slope $m = 6$ and the y-intercept $b = 0$, we can write the complete linear equation: $y = 6x + 0$ $y = 6x$
$y = 6x + 0$
More Information
The equation $y = 6x$ means that for every increase of 1 in x, y increases by 6. In this case, the y-intercept turns out to be zero, so y is simply 6 times x.
Tips
A common mistake is incorrectly calculating the slope, for example by swapping the x and y differences in the slope formula. Another might be making an arithmetic error while solving for the y-intercept.
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