Find the x and y intercepts of the equation 2x + 3y = 6, and the answers at the end.
Understand the Problem
The user is asking for a linear equation, and requests that we solve for the x and y intercepts, finally providing the answers.
Answer
$x$-intercept: $(-2, 0)$ $y$-intercept: $(0, 4)$
Answer for screen readers
$x$-intercept: $(-2, 0)$ $y$-intercept: $(0, 4)$
Steps to Solve
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General form of a linear equation
A linear equation can be written in the form $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. Let's use the example equation $y = 2x + 4$.
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Finding the y-intercept
The $y$-intercept is the point where the line crosses the $y$-axis. This occurs when $x = 0$. Substitute $x = 0$ into the equation and solve for $y$:
$y = 2(0) + 4$ $y = 4$
So, the $y$-intercept is $4$, and the coordinate is $(0, 4)$.
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Finding the x-intercept
The $x$-intercept is the point where the line crosses the $x$-axis. This occurs when $y = 0$. Substitute $y = 0$ into the equation and solve for $x$:
$0 = 2x + 4$
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Solve for x
Subtract 4 from both sides:
$-4 = 2x$
Divide both sides by 2:
$x = -2$
So, the $x$-intercept is $-2$, and the coordinate is $(-2, 0)$.
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Summary of intercepts
The $y$-intercept is $(0, 4)$ and the $x$-intercept is $(-2, 0)$.
$x$-intercept: $(-2, 0)$ $y$-intercept: $(0, 4)$
More Information
The intercepts are useful for graphing the line. You can plot these two points on a coordinate plane and draw a straight line through them. This line represents the equation $y = 2x + 4$.
Tips
A common mistake is confusing the $x$ and $y$ intercepts. Remember, to find the $x$-intercept, set $y = 0$, and to find the $y$-intercept, set $x = 0$. Also, be careful with the signs when solving for $x$ and $y$.
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