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Chapter 3: Problem 88

Use slope-intercept graphing to graph the equation. $$ y=-4 x+2 $$

Short Answer

Expert verified
Plot y-intercept at (0, 2); use slope -4 to find another point (1, -2); draw line through both points.

Step by step solution

01

- Identify the Slope and Y-Intercept

Examine the given equation and identify the slope and y-intercept. The equation is in the slope-intercept form, which is defined as y = mx + b,where m is the slope and b is the y-intercept. For the equation given, y = -4x + 2,the slope (m) is -4 and the y-intercept (b) is 2.
02

- Plot the Y-Intercept

Plot the y-intercept (0, 2) on the graph. This point is where the line crosses the y-axis.
03

- Use the Slope to Find Another Point

Use the slope to find another point on the line. The slope is -4, which can be understood as -4/1. This means that for every 1 unit you move to the right on the x-axis, you move 4 units down on the y-axis. Starting from the y-intercept (0, 2), move 1 unit to the right to (1, 2) and then 4 units down to (1, -2). Plot the point (1, -2).
04

- Draw the Line

Draw a straight line through the points (0, 2) and (1, -2). This line represents the equation y = -4x + 2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Linear Equations
Graphing linear equations is a fundamental concept in algebra. A linear equation, such as the one given in the problem, can be written in slope-intercept form: y = mx + b. Here, 'm' represents the slope and 'b' represents the y-intercept. Understanding these two components is key to graphing the equation accurately.
The Slope
The slope of a line indicates its steepness and direction. In the equation y = -4x + 2, the slope is -4. Slope can be thought of as 'rise over run' which describes how much the line goes up or down for every unit it moves horizontally. A negative slope means the line will descend as it moves to the right.

In our case, the slope of -4 can be written as the fraction -4/1, meaining for every 1 unit to the right, we move 4 units down.
Plotting Points: The Y-Intercept
The y-intercept is the point where the line crosses the y-axis. For the equation y = -4x + 2, the y-intercept is 2. This is where you start your graph.

To plot the y-intercept, locate the point (0, 2) on the coordinate plane. This means when x = 0, y = 2. Place a dot at this point.
Using the Coordinate Plane
To graph a linear equation, you'll use a coordinate plane, which is a grid defined by a horizontal x-axis and a vertical y-axis. Each point on the plane can be identified by an ordered pair (x, y).

After plotting the y-intercept (0, 2), use the slope to find another point. From (0, 2), move 1 unit right (to x = 1) and 4 units down to (1, -2).

Finally, draw a line through these points. This line is the graphical representation of the equation y = -4x + 2.

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Most popular questions from this chapter

For exercises 9鈥�20, (a) graph the given points, and draw a line through the points. (b) use the graph to find the slope of the line. (c) use the slope formula to find the slope of the line. \((1,4) ;(3,10)\)

(a) graph the given points, and draw a line through the points. (b) use the graph to find the slope of the line. (c) use the slope formula to find the slope of the line. \((-20,-50) ;(10,30)\)

Solve. \(m=\frac{6-6}{4-9}\)

(a) find three solutions of the equation. (b) graph the equation. \(y=-x\)

(a) find three solutions of the equation. (b) graph the equation. \(y=-\frac{1}{3} x+5\)
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