Problem 90 In the following exercises, grap... [FREE SOLUTION]

Chapter 4: Problem 90

In the following exercises, graph by plotting points. $4 x+y=-5$

Short Answer

Expert verified

Plot points (-2, 3), (-1, -1), (0, -5), (1, -9), (2, -13) and draw a line through them.

Step by step solution

- Rearrange the Equation

First, solve the given equation for y in terms of x. Start with the equation: 4x + y = -5Subtract 4x from both sides to isolate y: y = -4x - 5

- Create a Table of Values

Choose several values for x to find corresponding y-values. This helps to plot points on the graph. For instance, choose x-values -2, -1, 0, 1, 2 and solve for y:For x = -2: y = -4(-2) - 5 = 8 - 5 = 3For x = -1: y = -4(-1) - 5 = 4 - 5 = -1For x = 0: y = -5For x = 1: y = -4(1) - 5 = -4 - 5 = -9For x = 2: y = -4(2) - 5 = -8 - 5 = -13

- Plot the Points

Plot the points (-2, 3), (-1, -1), (0, -5), (1, -9),(2, -13) on the coordinate plane.

- Draw the Line

After plotting the points, draw a straight line through them to represent the equation 4x + y = -5.

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Key Concepts

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

Plotting Points

Plotting points is an essential skill when graphing linear equations. When you plot a point, you use a pair of coordinates $(x, y)$. The x-value tells you how far to move horizontally from the origin, and the y-value tells you how far to move vertically.

For instance, the point (-2, 3) means you move 2 units to the left (since it's negative) and then 3 units up. Plotting is straightforward if you break it down into small steps. Always double-check your plotted points to ensure accuracy.

Remember:

The first value is the x-coordinate.
The second value is the y-coordinate.

Practice makes perfect, so the more you plot points, the easier it will become.

Coordinate Plane

The coordinate plane is a two-dimensional surface where we can plot points, lines, and curves. It consists of two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical). They intersect at the origin $(0,0)$.

To remember the layout:

The right side of the origin is positive x-values; the left side is negative.
Above the origin are positive y-values; below are negative y-values.

The plane is divided into four quadrants, helping you locate points accurately.

When graphing a linear equation, always use a well-labeled coordinate plane with evenly spaced intervals. Neatness counts!

Slope-Intercept Form

The slope-intercept form of a linear equation is superb for graphing because it shows the slope and y-intercept directly. The standard form is: $$ y = mx + b $$

Here:

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91影视

In the following exercises, graph by plotting points. \(4 x+y=-5\)

Short Answer

Step by step solution

- Rearrange the Equation

- Create a Table of Values

- Plot the Points

- Draw the Line

Key Concepts

Plotting Points

Coordinate Plane

Slope-Intercept Form

One App. One Place for Learning.

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