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Chapter 3: Problem 1

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(4,7) \text { and }(8,10)$$

Short Answer

Expert verified
The slope of the line passing through the points (4,7) and (8,10) is 3/4. The line rises.

Step by step solution

01

Identify the coordinates

Firstly, identify the coordinates of the two points. The coordinates of the first point are \( x_1=4 \) and \( y_1=7 \); the coordinates of the second point are \( x_2=8 \) and \( y_2=10 \).
02

Calculate the slope

Secondly, use the formula for the slope of a line \( m = (y2-y1)/(x2-x1) \). Thus, substituting the values we have, we get \( m = (10 - 7) / (8 - 4) = 3/4 \).
03

Determine the direction of the line

Finally, as the calculated slope is positive, this means that the line is rising. A positive slope indicates a line that goes up from left to right.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The line through \((2,2)\) and the origin has slope 1

Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through \((-5,6)\) and is perpendicular to the line that has an \(x\) -intercept of 3 and a \(y\) -intercept of \(-9\).

Exercises \(82-84\) will help you prepare for the material covered in the next section. In each exercise, solve for \(y\) and put the equation in slope- intercept form. $$y+3=-\frac{3}{2}(x-4)$$

Describe the graph of \(y=200\).

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-8,-10)\) and parallel to the line whose equation is \(y=-4 x+3\)
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