Question

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

Name: Problem 50, Chapter 1: Applied Calculus for the Managerial, Life, and Social Sciences
Uploaded: 2021-05-11T16:36:15-08:00
Duration: 3 min 46 s
Channel: Naresh Bagrecha
Description: Find an equation of the line that satisfies the given condition. The line passing through the origin and parallel to the line joining the points (2,4) and (4,7)

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

Applied Calculus for the Managerial, Life, and Social Sciences

Soo T. Tan 10th Edition

Chapter 1, Problem 50

Instant Answer

Solved by Expert Naresh Bagrecha

05/11/2021

Step 1

The formula for the slope (m) between two points (x1,y1) and (x2,y2) is given by: \[m = \frac{y2 - y1}{x2 - x1}\] Substituting the given points into the formula, we get: \[m = \frac{7 - 4}{4 - 2} = \frac{3}{2}\] Show more…

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

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Key Concepts

Slope Calculation

The slope of a line represents its steepness and is calculated as the change in the vertical direction divided by the change in the horizontal direction between any two points on the line. This concept is fundamental for determining the rate at which y changes with respect to x in any linear situation.

Parallel Lines

Parallel lines are lines in the same plane that do not intersect, which means they maintain a constant distance apart. In terms of algebra, this property is characterized by equal slopes; if two lines are parallel, they have identical slopes.

Point-Slope Form

The point-slope form is a method for writing the equation of a line when one point on the line and the slope are known. Expressed as y - y? = m(x - x?), it offers a straightforward way to define a line's equation using its slope (m) and a given point (x?, y?).

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