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 ?)



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 ?)

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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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