Susan traveled 57.9 miles each day for the past 7 days. How many miles did she travel in all?
1 answer:
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Given:
The table of values.
To find:
The equation that best represents the relationship.
Solution:
From the given table it is clear that the value of x increasing by 2 and the value of y increasing by 3. Since y is increasing at a constant rate with respect to x, therefore the given table represents a linear relationship.
Consider any two points from the given table. Let the two points are (2,2) and (4,5). So, the equation of the line is
On further simplification, we get
Therefore, the correct option is A.
Remark
Secants going through a circle form a ratio that's the same for all secants going through the circle and beginning at 1 point. See the diagram below for the ratio. Follow the Line designations carefully. This comes up many times.
General Ratio is (segment from the external point to the the first intersect point of the circumference divided by the distance from the external point to the second intercept point on the circumference).
General Ratio
Put in terms of the diagram the general ratio is (OA / OB)
Equation
OA/OB = OC/OD
Substitute and Solve
9/(9 + 11) = 10/(10 + x)
9/20 = 10/(10 + x) Notice that you can't combine the right side. Cross Multiply
9*(10 + x) = 10 * 20 Remove the brackets on the left. Combine the right factors.
90 + 9x = 200 Subtract 90 from both sides.
9x = 200 - 90
9x = 110 Divide by 9
110 / 9 = 12.22
Secants going through a circle form a ratio that's the same for all secants going through the circle and beginning at 1 point. See the diagram below for the ratio. Follow the Line designations carefully. This comes up many times.
General Ratio is (segment from the external point to the the first intersect point of the circumference divided by the distance from the external point to the second intercept point on the circumference).
General Ratio
Put in terms of the diagram the general ratio is (OA / OB)
Equation
OA/OB = OC/OD
Substitute and Solve
9/(9 + 11) = 10/(10 + x)
9/20 = 10/(10 + x) Notice that you can't combine the right side. Cross Multiply
9*(10 + x) = 10 * 20 Remove the brackets on the left. Combine the right factors.
90 + 9x = 200 Subtract 90 from both sides.
9x = 200 - 90
9x = 110 Divide by 9
110 / 9 = 12.22