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Chapter 11: Problem 219

Show that the slope of the segment joining \((1,2)\) and \((2,6)\) is equal to the slope of the segment joining \((5,15)\) and \((10,35)\)

Short Answer

Expert verified
The slopes of the segments joining \((1,2)\) and \((2,6)\) and \((5,15)\) and \((10,35)\) are equal, as we calculated both slopes to be 4 using the slope formula \( slope = \frac{y_2-y_1}{x_2-x_1} \).

Step by step solution

01

Find the slope of the segment joining \((1,2)\) and \((2,6)\)

Using the slope formula, we substitute the values from the given coordinates: \( slope_1 = \frac{6-2}{2-1} \) Now, perform the subtraction in the numerator and denominator: \( slope_1 = \frac{4}{1} \) So, the slope of this segment is: \( slope_1 = 4 \)
02

Find the slope of the segment joining \((5,15)\) and \((10,35)\)

Now, we will calculate the slope of the second segment using the given coordinates and the slope formula: \( slope_2 = \frac{35-15}{10-5} \) Subtract the coordinates in the numerator and denominator: \( slope_2 = \frac{20}{5} \) So, the slope of this segment is: \( slope_2 = 4 \)
03

Compare the two slopes

Now that we have the slopes of both segments, we can compare them to determine if they are equal: \( slope_1 = slope_2 \) Since both slopes are equal to 4, the statement is true. The slopes of the segments joining \((1,2)\) and \((2,6)\) and \((5,15)\) and \((10,35)\) are equal.

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Most popular questions from this chapter

Find the equation of the line which passes through the points \((-3,1)\) and \((7,11)\)

Graph the function defined by \(3 \mathrm{x}-4 \mathrm{y}=12\)

Find the slope and Y-intercept of the following lines. (a) \(\mathrm{y}=3 \mathrm{x}-1\) (b) \(\mathrm{y}=1-4 \mathrm{x}\) (c) \(2 \mathrm{y}=4 \mathrm{x}+7\)

Find the equation of the line passing through the points \((2,5)\) and \((6,2)\). Check the results graphically.

Write the equation in slope-intercept form; specify the slope and the \(y\) -intercept of the line. Sketch the graph of the equation. \(2 \mathrm{x}-3 \mathrm{y}=5\)
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