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Chapter 3: Problem 52

Describe how to calculate the slope of a line passing through two points.

Short Answer

Expert verified
The slope of a line passing through two points is calculated by the formula \((y_2 - y_1) / (x_2 - x_1)\), which is the change in 'y' divided by the change in 'x' between two points.

Step by step solution

01

Understand the Slope Formula

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula \((y_2 - y_1) / (x_2 - x_1)\). This formula is derived from the definition of 'slope' as the 'change in y' divided by the 'change in x' between two points on a line.
02

Identify the Two Points

Start by identifying the two points. Let's assume that these two points are given as (x1, y1) and (x2, y2).
03

Plug the Coordinates into the Formula

Substitute the coordinates of the two points into the slope formula. Specifically, replace x1, y1, x2, and y2 in the formula \((y_2 - y_1) / (x_2 - x_1)\) with the coordinates of the given points.
04

Perform the Subtractions

Subtract the y1 value from the y2 value for the numerator and the x1 value from the x2 value for the denominator.
05

Unravel the Slope

Finally, divide the difference of y's by the difference of x's to work out the slope.

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Most popular questions from this chapter

Write an equation in slope-intercept form of the line satisfying the given conditions. What is the slope of a line that is perpendicular to the line whose equation is \(A x+B y=C, A \neq 0\) and \(B \neq 0 ?\)

Use a graphing utility to graph each equation.Then use the \([\text { TRACE }]\) feature to trace along the line and find the coordinates of two points. Use these points to compute the line's slope. $$y=2 x+4$$

What is a \(y\) -intercept of a graph?

Use a graphing utility to graph each equation. You will need to solve the equation for \(y\) before entering it. Use the graph displayed on the screen to identify the \(x\) -intercept and the \(y\) -intercept. $$3 x-y=9$$

Write an equation in slope-intercept form of the line satisfying the given conditions. The line is perpendicular to the line whose equation is \(3 x-2 y=4\) and has the same y-intercept as this line.
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