How to Find x- and y-intercepts in the Standard Form of Equation?
In this comprehensive and step-by-step guide, you will learn how to find \(x\)- and \(y\)-intercepts when the standard form of equations is provided.
The standard form of a linear equation in two variables is typically written as \(Ax + By = C\), where \(A, B\), and \(C\) are constants and \(x\) and \(y\) are the variables. This form is sometimes also referred to as the “general form” or “standard linear form”.
A Step-by-step guide to find \(x\)- and \(y\)-intercepts in the standard form of equation
In the standard form of the equation, it is not immediately clear what the \(x\)- and \(y\)-intercepts of the graph of the equation are. However, it is still possible to find them using algebraic techniques.
To find the \(x\)-intercept, we need to find the value of \(x\) when \(y = 0\). This means we can substitute \(0\) for \(y\) in the equation and solve for \(x\). The resulting value of \(x\) will be the \(x\)-intercept.
To find the \(y\)-intercept, we need to find the value of \(y\) when \(x = 0\). This means we can substitute \(0\) for \(x\) in the equation and solve for \(y\). The resulting value of \(y\) will be the \(y\)-intercept.
Finding \(x\)- and \(y\)-intercepts in the Standard Form of Equation – Examples 1
Find the \(x\)- and \(y\)-intercepts of the line \(2x + 3y = 6\)
Solution:
To find the \(x\)-intercept, we set \(y = 0\) and solve for \(x\):
\(2x + 3(0) = 6\)
\(2x = 6\)
\(x = 3\)
So, the \(x\)-intercept is \((3, 0)\).
To find the \(y\)-intercept, we set \(x = 0\) and solve for \(y\):
\(2(0) + 3y = 6\)
\(3y = 6\)
\(y = 2\)
So, the \(y\)-intercept is \((0, 2)\).
Therefore, the graph of the equation \(2x + 3y = 6\) intersects the \(x\)-axis at \((3, 0)\) and the \(y\)-axis at \((0, 2)\).
Exercises for Finding \(x\)- and \(y\)-intercepts in the Standard Form of Equation
Find the \(x\)- and \(y\)-intercepts of each line.
- \(\color{blue}{2x+y=-4}\)
- \(\color{blue}{x-y=6}\)
- \(\color{blue}{3x-2y=18}\)
- \(\color{blue}{\left(-2,\:0\right), \left(0,\:-4\right)}\)
- \(\color{blue}{\left(6,\:0\right), \left(0,\:-6\right)}\)
- \(\color{blue}{\left(6,\:0\right), \left(0,\:-9\right)}\)
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