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Chapter 1: Problem 58

Sketch the straight line defined by the linear equation by finding the \(x\) - and \(y\) -intercepts. $$ 2 x-5 y+10=0 $$

Short Answer

Expert verified
The x-intercept is found by setting y = 0 and solving for x, resulting in the point \((-5, 0)\). The y-intercept is found by setting x = 0 and solving for y, resulting in the point \((0, 2)\). To sketch the line, plot these points on the coordinate plane and draw a straight line through them.

Step by step solution

01

Find the x-intercept.

To find the x-intercept, we need to set y = 0 in the given equation and solve for x: \(2x - 5(0) + 10 = 0\) This simplifies to: \(2x + 10 = 0\) Now, solve for x: \(2x = -10\) \(x = -5\) So, the x-intercept is \((-5, 0)\).
02

Find the y-intercept.

To find the y-intercept, we need to set x = 0 in the given equation and solve for y: \(2(0) - 5y + 10 = 0\) This simplifies to: \(-5y + 10 = 0\) Now, solve for y: \(-5y=-10\) \(y = 2\) So, the y-intercept is \((0, 2)\).
03

Sketch the line.

Now that we have both the x-intercept and y-intercept, let's sketch the straight line. To do this, plot the points (-5, 0) and (0, 2) on the coordinate plane as these represent the points where the line crosses the x-axis and y-axis, respectively. Then, draw a straight line through these points, extending it to the edges of your coordinate plane. And there you have it! You've successfully sketched the straight line defined by the linear equation \(2x - 5y + 10 = 0\).

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