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Chapter 4: Problem 179

Graph using the intercepts. \(-x+5 y=10\)

Short Answer

Expert verified
Intercepts: (10, 0) and (0, 2); draw the line through them.

Step by step solution

01

- Find the x-intercept

To find the x-intercept, set y to 0 in the equation ostrip_duplication_tag\(-x + 5y = 10\)Set y = 0 and solve for x: o/x = 10Thus, the x-intercept is (10, 0).
02

- Find the y-intercept

To find the y-intercept, set x to 0 in the equation o/x - + 5y = 10Set x = 0 and solve for y: ory/y = 2Thus, the y-intercept is (0, 2).
03

- Plot the intercepts

On a Cartesian plane, plot the points (10, 0) and (0, 2).
04

- Draw the line

Draw a straight line passing through the points (10, 0) and (0, 2), extending in both directions.

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Key Concepts

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

x-intercept
Let's start with finding the x-intercept. The x-intercept is the point where the graph of an equation crosses the x-axis. This means at this point, the y-value is zero.
To find the x-intercept for the equation \(-x + 5y = 10\), we set y to 0 and solve for x:
\(-x + 5(0) = 10\) simplifies to \(鈥搙 = 10\).
Solving for x, we get \(x = 鈥�10\).
Thus, the x-intercept is the point \((10, 0)\).
The x-intercept tells us where the line will meet the x-axis.
y-intercept
Next, we'll find the y-intercept. The y-intercept is the point where the graph crosses the y-axis. This means at this point, the x-value is zero.
To find the y-intercept for the equation \(-x + 5y = 10\), we set x to 0 and solve for y:
\(-0 + 5y = 10\) simplifies to \(5y = 10\).
Solving for y, we get \(y = 2\).
So, the y-intercept is the point \((0, 2)\).
The y-intercept informs us where the line will touch the y-axis.
plotting points
Now that we have both intercepts, the next step is to plot these points on the Cartesian plane. The Cartesian plane has an x-axis (horizontal) and a y-axis (vertical).
To plot, follow these steps:
  • Start at the origin (0, 0).
  • Mark the x-intercept \(10, 0)\) on the x-axis.
  • Mark the y-intercept \(0, 2)\) on the y-axis.
These are the points where the line crosses the axes. Accurately plotting these points is crucial in graphing the line correctly.
graphing linear equations
Finally, we can graph the linear equation by drawing a line through the plotted points \((10, 0)\) and \((0, 2)\).
Here's how to do it:
  • Use a ruler to ensure the line is straight.
  • Extend the line through the entire graph, in both positive and negative directions if needed.
  • Label the line with its equation \(-x + 5y = 10\).
Graphing helps visualize the solutions of the equation. Just using intercepts is a straightforward strategy to draw these lines accurately.

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