Question
The equation of a line is given below. \[ 2 x+y=6 \] Find the \( x \)-intercept and the \( y \)-intercept. Then use them to graph the line. \( x \)-intercept:
Ask by Kelley Mullins. in the United States
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The x-intercept is (3, 0) and the y-intercept is (0, 6). Plot these points on a graph and draw a straight line through them.
Solution
To find the x-intercept, set y = 0 in the equation:
2x + y = 6
2x + 0 = 6
2x = 6
x = 3
Thus, the x-intercept is (3, 0).
For the y-intercept, set x = 0:
2(0) + y = 6
y = 6
So, the y-intercept is (0, 6).
To graph the line, plot the points (3, 0) and (0, 6) on a coordinate plane and draw a straight line that passes through them.
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Simplify this solution Bonus Knowledge
To find the \( x \)-intercept, set \( y = 0 \) in the equation \( 2x + y = 6 \). This gives us \( 2x + 0 = 6 \), leading to \( x = 3 \). So, the \( x \)-intercept is \( (3, 0) \). Now, for the \( y \)-intercept, set \( x = 0 \) in the same equation. This results in \( 2(0) + y = 6 \), simplifying to \( y = 6 \). Thus, the \( y \)-intercept is \( (0, 6) \). Plotting these points on a graph, you can draw a straight line through \( (3, 0) \) and \( (0, 6) \). Voilà, you have your line!
