91Ó°ÊÓ

To find the x-intercept of a linear equation, you need to set the value of y to 0. This essentially gives you the point where the line crosses the x-axis. Here's how you do it:

Start with the equation \[ 2x + 5y = 10 \]
Substitute y = 0 to isolate x: \[ 2x + 5(0) = 10 \]
Solve for x:
\[ 2x = 10 \]
\[ x = 5 \]

This tells us that the x-intercept is at the point (5, 0). This is where the line will cross the x-axis on a graph. Remember, to find the x-intercept: * Set y to 0 in your equation * Solve the resulting equation for x

To find the y-intercept of a linear equation, you need to set the value of x to 0. This gives you the point where your line crosses the y-axis. Let's break it down step-by-step:

Start with the same equation: \[ 2x + 5y = 10 \]
Set x = 0: \[ 2(0) + 5y = 10 \]
Now solve for y:
\[ 5y = 10 \]
\[ y = 2 \]
This tells us that the y-intercept is at the point (0, 2). This is where the line will cross the y-axis on a graph. To summarize, to find the y-intercept: * Set x to 0 in your equation * Solve the resulting equation for y

Graphing a line involves finding at least two points that lie on the line, plotting these points, and then drawing a straight line through them. For the equation \[ 2x + 5y = 10 \], we've found the intercepts at (5, 0) and (0, 2). Follow these steps:

• First, plot the x-intercept (5, 0) on the x-axis.
• Next, plot the y-intercept (0, 2) on the y-axis.
• Finally, draw a straight line through these points.

This is the line representing your equation. It's always a good idea to plot the intercepts first, as it simplifies the process and ensures accuracy.

Solving linear equations means finding the values of x and y that make the equation true. Here’s a step-by-step method:

1. Isolate one variable: To find the x-intercept, we set y to 0 and solved for x. To find the y-intercept, we set x to 0 and solved for y.
2. Substitute and simplify: By substituting 0 for one variable, the equation simplifies and makes it easier to solve for the other variable.
3. Solve for the remaining variable: Just do the arithmetic to isolate the variable on one side of the equation.

Recall the steps for our examples: * For the x-intercept: \[ 2x + 5(0) = 10 \] \[ 2x = 10 \] \[ x = 5 \] * For the y-intercept: \[ 2(0) + 5y = 10 \] \[ 5y = 10 \] \[ y = 2 \] These results are the solutions that help us graph the line accurately.