Question
Write the linear equation that gives the rule for this table.
x y
52 39
61 48
70 57
79 66
Write your answer as an equation with y first, followed by an equals sign.
x y
52 39
61 48
70 57
79 66
Write your answer as an equation with y first, followed by an equals sign.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the linear equation that models the relationship between \(x\) and \(y\) in the given table, we need to determine the slope and y-intercept.
1. **Calculate the slope (m):**
Using the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the first two points (52, 39) and (61, 48):
\[
m = \frac{48 - 39}{61 - 52} = \frac{9}{9} = 1
\]
2. **Find the y-intercept (b):**
We can use the slope-intercept form of the equation:
\[
y = mx + b
\]
We know \(m = 1\). Now we can use one of the points to find \(b\). Using the point (52, 39):
\[
39 = 1(52) + b
\]
\[
b = 39 - 52 = -13
\]
3. **Write the equation:**
Now that we have the slope and y-intercept, we can write the equation:
\[
y = 1x - 13
\]
Thus, the linear equation is:
\[
y = x - 13
\]
1. **Calculate the slope (m):**
Using the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the first two points (52, 39) and (61, 48):
\[
m = \frac{48 - 39}{61 - 52} = \frac{9}{9} = 1
\]
2. **Find the y-intercept (b):**
We can use the slope-intercept form of the equation:
\[
y = mx + b
\]
We know \(m = 1\). Now we can use one of the points to find \(b\). Using the point (52, 39):
\[
39 = 1(52) + b
\]
\[
b = 39 - 52 = -13
\]
3. **Write the equation:**
Now that we have the slope and y-intercept, we can write the equation:
\[
y = 1x - 13
\]
Thus, the linear equation is:
\[
y = x - 13
\]
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