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Chapter 1: Problem 50

Find an equation of the line that satisfies the given condition. The line passing through the origin and parallel to the line passing through the points \((2,4)\) and \((4,7)\)

Short Answer

Expert verified
The equation of the line passing through the origin and parallel to the line passing through the points \((2,4)\) and \((4,7)\) is: \(y = \frac{3}{2}x\)

Step by step solution

01

Find the slope of the line passing through \((2,4)\) and \((4,7)\)

To find the slope of the line passing through the two given points, use the formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\) Here, \((x_1, y_1) = (2,4)\) and \((x_2, y_2) = (4,7)\). Substitute the values and find the slope: \(m = \frac{7 - 4}{4 - 2} = \frac{3}{2}\) The slope of the line passing through \((2,4)\) and \((4,7)\) is \(\frac{3}{2}\).
02

Use the slope-point form

Since the line we are looking for is parallel to the one found in step 1, it will have the same slope. Therefore, \(m = \frac{3}{2}\). The line passes through the origin, so the point \((0,0)\) is on our line. Now, we can use the slope-point form of the equation of a line: \(y - y_1 = m(x - x_1)\) Substitute the values for point \((x_1, y_1) = (0,0)\) and the slope \(m = \frac{3}{2}\): \(y - 0 = \frac{3}{2}(x - 0)\) Simplify to get the equation of the line: \(y = \frac{3}{2}x\)
03

Final answer

The equation of the line passing through the origin and parallel to the line passing through the points \((2,4)\) and \((4,7)\) is: \(y = \frac{3}{2}x\)

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Most popular questions from this chapter

The line with equation \(A x+B y+C=0(B \neq 0)\) and the line with equation \(a x+b y+c=0(b \neq 0)\) are parallel if \(A b-a B=0 .\)

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