Question

Find the rule that connects the first number to the second number of each pair. Apply the rule to find the missing number in the third pair. $18 is to 22$ $54 is to 26$ $9 is to ?$

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Answer to a math question Find the rule that connects the first number to the second number of each pair. Apply the rule to find the missing number in the third pair. $18 is to 22$ $54 is to 26$ $9 is to ?$

Maude
4.7
To find the equation of the line that passes through the points $18,22$ and $54,26$, we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

Step 1: Find the slope $m$

The slope $m$ of a line passing through two points $x1, y1$ and $x2, y2$ is given by the formula:

m = \frac{y2 - y1}{x2 - x1}

Using the points $18,22$ and $54,26$, we have:

m = \frac{26 - 22}{54 - 18}
m = \frac{4}{36}
m = \frac{1}{9}

Step 2: Find the y-intercept $b$

We can use the point-slope form of a linear equation to find b:

y - y1 = m$x - x1$

Using the point $18,22$, we have:

y - 22 = \frac{1}{9}$x - 18$
y - 22 = \frac{1}{9}$x$ - 2
y = \frac{1}{9}x + 20

Therefore, the equation of the line passing through the points $18,22$ and $54,26$ is:

y = \frac{1}{9}x + 20

To find the point whose abscissa is 9, we substitute x = 9 into the equation above:

y = \frac{1}{9}$9$ + 20
y = 1 + 20
y = 21

Therefore, the point whose abscissa is 9 is $9,21$.

Answer: The equation of the line is y = \frac{1}{9}x + 20 and the point with an abscissa of 9 is $9,21$.

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