91Ó°ÊÓ

The y-intercept is a critical concept in graphing linear equations. It is the point at which the graph crosses the y-axis. This happens when the value of x is zero in the equation. In other words, to find the y-intercept, we set x to 0 and solve for y.

For the given equation:
\text\textbf\tex\tex {2 + 3x = 2y}\text \ we set x = 0 to get:
\text\textbf\tx\tsx(0)\text {2 + 3(0) = 2y}\text \ Simplifying this, we get: \text\textbf\ty\ty(1)\text {2 = 2y}\text \ Divide both sides by 2: \text\textbf\ty\text \((y = 1)\) \
This means the y-intercept is at \(\text \)\boldmathtext\text\text$${(0, 1)\text} \
It is useful to remember that the y-intercept is always written as a point where x-coordinates are zero.

The x-intercept is the point where the graph crosses the x-axis. This happens when the value of y is zero in the equation. To find the x-intercept, we set y to 0 and solve for x.

For our equation:
\text\textbf\ty\ty{2 + 3x = 2y}\text \ replace y with 0 to get:
\text\tx\text {2 + 3x = 2(0)} \ Simplifying this equation:
\text\ty\text\text \(2 + 3x = 0\) \
Move the 2 to the other side:
\text\text\(\text {3x = -2}\text \) Divide both sides by 3: \text\text\text$$( \(x - \frac{2}{3}\text)} \
So the x-intercept is: \)\text $${-(\frac{2}{3}, 0)\text} Always remember to write the x-coordinate for the intercept with y = 0.

Solving linear equations is a fundamental skill in algebra. A linear equation can be written in the form \(ax + by = c\). Solving such equations reveals the point(s) at which a graph crosses the axes.

The basic steps involve:

• Isolating the variable you're solving for
• Performing operations like addition, subtraction, multiplication, or division to both sides
• Simplifying the equation step-by-step

In our example:
\(2 + 3x = 2y\) \ To find the y-intercept, solve for y when \(x=0\). Conversely, to find the x-intercept, solve for \(x\) when y = 0. Always understand the purpose of each step in solving these equations. This will help you in graphing and interpreting linear equations effectively.