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Chapter 1: Problem 6

Find the slope of the line that passes through the given pair of points. $$ (4,5) \text { and }(3,8) $$

Short Answer

Expert verified
The slope of the line that passes through the points (4,5) and (3,8) is -3.

Step by step solution

01

Identify the coordinates of the points given

The given points are (4,5) and (3,8). We can denote these as (x1, y1) and (x2, y2) respectively: \(x1 = 4\) \(y1 = 5\) \(x2 = 3\) \(y2 = 8\)
02

Substitute the coordinates into the slope formula

Now we can substitute the coordinates into the slope formula: $$ m = \frac{y2 - y1}{x2 - x1} = \frac{8 - 5}{3 - 4} $$
03

Simplify and calculate the slope

We can now simplify the expression and solve for the slope, m: $$ m = \frac{3}{-1} = -3 $$ So, the slope of the line that passes through the points (4,5) and (3,8) is -3.

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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. $$ 2 x+4 y=14 $$

At a unit price of \(\$ 55\), the quantity demanded of a certain commodity is 1000 units. At a unit price of \(\$ 85\), the demand drops to 600 units. Given that it is linear, find the demand equation. Above what price will there be no demand? What quantity would be demanded if the commodity were free?

The relationship between the temperature in degrees Fahrenheit \(\left({ }^{\circ} \mathrm{F}\right)\) and the temperature in degrees Celsius \(\left({ }^{\circ} \mathrm{C}\right)\) is $$ F=\frac{9}{5} C+32 $$ a. Sketch the line with the given equation. b. What is the slope of the line? What does it represent? c. What is the \(F\) -intercept of the line? What does it represent?

Is there a difference between the statements "The slope of a straight line is zero" and "The slope of a straight line does not exist (is not defined)"? Explain your answer.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If the data consist of two distinct points, then the leastsquares line is just the line that passes through the two points.
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