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Chapter 4: Problem 197

Graph using the intercepts. \(2 x-5 y=-20\)

Short Answer

Expert verified
The x-intercept is (-10, 0) and the y-intercept is (0, 4). Plot these points and draw a line through them.

Step by step solution

01

- Find the x-intercept

To find the x-intercept, set y to 0 in the equation and solve for x. Equation: 2x - 5(0) = -20 2x = -20 x = -10 The x-intercept is (-10, 0).
02

- Find the y-intercept

To find the y-intercept, set x to 0 in the equation and solve for y. Equation: 2(0) - 5y = -20 -5y = -20 y = 4 The y-intercept is (0, 4).
03

- Plot the intercepts

Plot the points (-10, 0) and (0, 4) on the coordinate plane. These points are your intercepts.
04

- Draw the line

Draw a straight line through the points (-10, 0) and (0, 4). This line represents the graph of the given equation.

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Key Concepts

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

x-intercept
The x-intercept is the point where a line crosses the x-axis. To find the x-intercept in a linear equation, set the value of y to 0 and solve for x. In our example, the equation is 2x - 5y = -20. By setting y to 0, the equation simplifies to 2x = -20, which means x = -10. This gives us the x-intercept as (-10, 0). This point tells us that when y is zero, x is -10.
y-intercept
The y-intercept is the point where a line crosses the y-axis. For finding the y-intercept, set the value of x to 0 and solve for y. Using the equation 2x - 5y = -20, if we set x to 0, the equation becomes -5y = -20. Solving for y, we get y = 4. Thus, the y-intercept is (0, 4). This indicates that when x is zero, y is 4.
coordinate plane
A coordinate plane is a two-dimensional plane formed by the intersection of a vertical y-axis and a horizontal x-axis. The plane is divided into four quadrants by these axes. Any point on the plane is identified by an ordered pair of numbers (x, y), which are called coordinates. Plotting points like the x-intercept (-10, 0) and the y-intercept (0, 4) involves locating these points on the coordinate plane. Once these points are plotted, they can be connected with a line to graph the equation.
linear equation
A linear equation is an equation that forms a straight line when graphed on a coordinate plane. It typically looks like Ax + By = C, where A, B, and C are constants. For the equation 2x - 5y = -20, the coefficients of x and y (2 and -5) dictate the slope and direction of the line. Solving for the intercepts helps in visualizing this line. After finding where the line crosses the x-axis and y-axis (intercepts), you plot these points and draw a line through them to represent the equation.

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