91Ó°ÊÓ

In mathematics, the x-intercept is where a graph crosses the x-axis. At this point, the y-value is always 0, because it lies on the x-axis. To find the x-intercept from an equation, you simply set y to 0 and solve for x.
Let's look at the provided equation: \ \[ x + y = 3 \] \ To find the x-intercept: \ 1. Set \( y = 0 \). \ 2. Substitute \( y = 0 \) into the equation. This becomes: \ \[ x + 0 = 3 \] \ 3. Solve for x: \ \[ x = 3 \] \ Therefore, the x-intercept is the point \( (3, 0) \).
Remember: \ - X-intercept is where the graph crosses the x-axis. \ - We set y to 0 to find it. \ - We then solve for x in the equation.

The y-intercept is where a graph crosses the y-axis. At this point, the x-value is always 0. To find the y-intercept from an equation, you set x to 0 and solve for y.
Let's use the given equation again: \ \[ x + y = 3 \] \ To find the y-intercept: \ 1. Set \( x = 0 \). \ 2. Substitute \( x = 0 \) into the equation. It becomes: \ \[ 0 + y = 3 \] \ 3. Solve for y: \ \[ y = 3 \] \ Therefore, the y-intercept is the point \( (0, 3) \).
A quick recap: \ - Y-intercept is where the graph crosses the y-axis. \ - We set x to 0 to find it. \ - We then solve for y in the equation.

Solving linear equations is foundational in algebra. A linear equation is one that forms a straight line when graphed. The general form is \ \[ ax + by = c \] \ where \(a\), \(b\), and \(c\) are constants. Let's focus on the key steps to solve these equations: \ 1. Identifying Intercepts: As discussed above, intercepts help in understanding the graph of the equation. \ - For the x-intercept, set y to 0 and solve for x. \ - For the y-intercept, set x to 0 and solve for y. \ 2. Substitution Method: \ - In this method, solve one equation for one variable and substitute this into the other equation. \ - This can be very useful for systems of equations. \ 3. Elimination Method: \ - Combine the equations to eliminate one of the variables. This is also helpful for systems of equations. \ 4. Graphical Method: \ - Equations can be graphed and the point of intersection gives the solution.
Understanding these basics ensures a strong foundation in solving linear equations. Remember to always check your solutions by substituting them back into the original equation.