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Chapter 1: Problem 9

Find the slope of the line that passes through the given pair of points. $$ (a, b) \text { and }(c, d) $$

Short Answer

Expert verified
The slope of the line passing through the given points \((a, b)\) and \((c, d)\) is: $$ m = \frac{d - b}{c - a} $$

Step by step solution

01

Write down the slope formula

The slope formula, denoted by m, is given by the equation: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ This equation helps in finding the slope of a line by dividing the change in the y-coordinates by the change in the x-coordinates.
02

Substitute the coordinates of the given points

Substitute the coordinates of the given points (a, b) as \((x_1, y_1)\) and (c, d) as \((x_2, y_2)\) in the slope formula. That is: $$ m = \frac{d - b}{c - a} $$
03

Simplify the expression for the slope

Since the given points are (a, b) and (c, d) and we've already substituted them into the slope formula, there are no further steps to simplify the expression. The slope of the line passing through the given points is: $$ m = \frac{d - b}{c - a} $$ This is the final answer, and the expression provided calculates the slope of the line passing through the points (a, b) and (c, d).

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Most popular questions from this chapter

Write the equation in the slopeintercept form and then find the slope and \(y\) -intercept of the corresponding line. $$ 2 x-3 y-9=0 $$

Find an equation of the line that passes through the point \((-2,2)\) and is parallel to the line \(2 x-4 y-8=0\).

Find conditions on \(a_{1}, a_{2}, b_{1}, b_{2}, c_{1}\), and \(c_{2}\) such that the system of linear equations $$ \begin{aligned} a_{1} x+b_{1} y &=c_{1} \\ a_{2} x+b_{2} y &=c_{2} \end{aligned} $$ has (a) no solution, (b) a unique solution, and (c) infinitely many solutions. Hint: Use the results of Exercise 33 .

Use the results of Exercise 63 to find an equation of a line with the \(x\) - and \(y\) -intercepts. $$ x \text { -intercept } 4 ; y \text { -intercept }-\frac{1}{2} $$

Find an equation of the line that satisfies the given condition. The line passing through \((-5,-4)\) and parallel to the line passing through \((-3,2)\) and \((6,8)\)
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