Problem 59
Question
a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. $$3 x+y-5=0$$
Step-by-Step Solution
Verified Answer
The equation in slope-intercept form is \( y = -3x + 5 \). The slope is \(-3\) and the y-intercept is \(5\).
1Step 1: Rewrite in Slope-Intercept Form
The first task is to change the equation \(3x + y - 5 = 0\) into slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Add \( -3x \) to both sides of the equation to get \( y = -3x + 5 \).
2Step 2: Identify the Slope and Y-Intercept
Now, in the slope-intercept form, from the equation \( y = -3x + 5 \), you can easily identify that the slope \(m\) is \(-3\) and the y-intercept \(b\) is \(5\).
3Step 3: Graph the Linear Function
To graph the linear function, first plot the y-intercept \(5\) on the y-axis. The slope \(-3\) can be understood as \(-3/1\); this means for every one step to the right on the x-axis, move three steps downwards. Following this method, plot more points. Finally, draw a line passing through these points, and that would be the graph of the function \( y = -3x + 5 \).
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Problem 59
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