/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 233 Construct the graph of the funct... [FREE SOLUTION] | 91影视

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Chapter 11: Problem 233

Construct the graph of the function defined by \(\mathrm{y}=3 \mathrm{x}-9\).

Short Answer

Expert verified
To construct the graph of \(y=3x-9\), start by plotting the y-intercept at point A(0, -9). The slope is 3, which means a rise of 3 units and a run of 1 unit. From A, find other points by moving up 3 units and right 1 unit to get point B(1, -6), point C(2, -3), and point D(3, 0). Draw a straight line passing through points A, B, C, and D to obtain the graph of the function \(y=3x-9\).

Step by step solution

01

Identify the type of function

The given equation y = 3x - 9 represents a linear function, as it has a variable x raised to the first power and a constant term.
02

Determine the slope and y-intercept

The equation is in the slope-intercept form (y = mx + b), which makes it easy to identify the slope (m) and the y-intercept (b). In this case, m = 3 and b = -9.
03

Plot the y-intercept

To plot the y-intercept, look for the point on the y-axis where the line crosses. Since b = -9, this point, usually noted by A, is (0, -9). Mark this point on the graph paper.
04

Use the slope to find more points along the line

The slope of the line is the ratio of the change in the y-coordinates to the change in the x-coordinates between any two points on the line (m = rise/run). Since our slope, m = 3, we can interpret it as a rise of 3 units and a run of 1 unit. Starting from the point A(0, -9), move up 3 units and right 1 unit to find a new point, B. The coordinates of point B would be (1, -6). Repeat this process to find a couple of more points, C and D, along the line (2, -3) and (3, 0).
05

Draw the line passing through the points

With the points A, B, C, and D plotted on the graph paper, use a ruler to draw a straight line passing through those points. This line represents the graph of the function y = 3x - 9.

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Most popular questions from this chapter

Find the slope and Y-intercept of the following lines. (a) \(\mathrm{y}=3 \mathrm{x}-1\) (b) \(\mathrm{y}=1-4 \mathrm{x}\) (c) \(2 \mathrm{y}=4 \mathrm{x}+7\)

Find the slope, the \(\mathrm{y}\) -intercept, and the \(\mathrm{x}\) -intercept of the equation \(2 x-3 y-18=0\)

Use the intercept form to graph \(3 \mathrm{x}+4 \mathrm{yx}=12\).

The slope and one point of a line are given. Is the Y-intercept positive or negative? (a) \(\mathrm{m}=22 / 7,(1, \pi)\) b) \(\mathrm{m}=\sqrt{2},(1,1.414)\)

Graph the function defined by \(3 \mathrm{x}-4 \mathrm{y}=12\)
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