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Chapter 0: Problem 5

Sketch the graphs of the equations. $$ x+y=1 $$

Short Answer

Expert verified
The graph of the equation \(x + y = 1\) is a straight line with a slope of -1 that goes through x-intercept (1, 0) and y-intercept (0, 1).

Step by step solution

01

Put the equation in slope-intercept form

To sketch the graph of the given equation, first we need to put the equation in the slope-intercept form, which is \(y = mx + b\), where m is the slope, and b is the y-intercept. Given equation: \(x + y = 1\) Subtract x from both sides of the equation: \(y = -x + 1\) Now, the equation is in the slope-intercept form with a slope(m) of -1 and a y-intercept(b) of 1.
02

Find the x-intercept and y-intercept

The x-intercept is the point where the graph intersects the x-axis, which means y = 0. The y-intercept is the point where the graph intersects the y-axis, which means x = 0. To find the x-intercept, set y = 0 and solve for x: \(0 = -x + 1\) Add x to both sides: \(x = 1\) So, the x-intercept is (1, 0). To find the y-intercept, set x = 0 and solve for y: \(y = -0 + 1\) So, the y-intercept is (0, 1).
03

Sketch the graph

Now, we have the slope, x-intercept, and y-intercept of the equation, which are enough to sketch the graph. 1. Plot the x-intercept (1, 0) and the y-intercept (0, 1) on the coordinate plane. 2. Draw the line that goes through these two points. 3. Label the graph with its equation, \(x + y = 1\). The graph is a straight line with a slope of -1 that goes through points (1, 0) and (0, 1).

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