Find the x-intercept and the y-intercept of the line x + 4y = 4. Then graph the line.
Understand the Problem
The question provides a linear equation, x + 4y = 4, and asks to find the x-intercept and y-intercept. Subsequently it requests to graph the line using these intercepts.
Answer
x-intercept: $4$ y-intercept: $1$
Answer for screen readers
x-intercept: $4$ y-intercept: $1$
Steps to Solve
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Find the x-intercept To find the x-intercept, set $y = 0$ in the equation and solve for $x$. $x + 4(0) = 4$ $x = 4$ The x-intercept is 4.
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Find the y-intercept To find the y-intercept, set $x=0$ in the equation and solve for $y$. $0 + 4y = 4$ $4y = 4$ $y = 1$ The y-intercept is 1.
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Graph the line Plot the x-intercept at $(4, 0)$ and the y-intercept at $(0, 1)$ on the coordinate plane. Draw a straight line passing through these two points.
x-intercept: $4$ y-intercept: $1$
More Information
The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Finding these intercepts helps in easily graphing the line.
Tips
A common mistake is to mix up the x and y values when calculating intercepts or plotting points. Remember that the x-intercept occurs when y = 0, and the y-intercept occurs when x = 0.
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