Graph each equation. x - 4y = 8

Verified step by step guidance

1. Step 1: The given equation is in the standard form of a linear equation, which is Ax + By = C. In this case, A=1, B=-4, and C=8.
2. Step 2: To graph this equation, it's often easiest to first convert it to slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, isolate y in the equation. You can do this by subtracting x from both sides and then dividing by -4.
3. Step 3: Once the equation is in slope-intercept form, identify the slope and the y-intercept. The slope is the coefficient of x, and the y-intercept is the constant term.
4. Step 4: Start by plotting the y-intercept on the y-axis. This is the point where the line crosses the y-axis.
5. Step 5: From the y-intercept, use the slope to find the next point. The slope is the rise over the run, meaning you go up or down (rise) and then right or left (run) to find the next point. Plot this point and draw a line through the two points. This line is the graph of the equation.

Key Concepts

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The general form is Ax + By = C, where A, B, and C are constants. In the given equation, x - 4y = 8, it represents a straight line when graphed on a coordinate plane.

Graphing Linear Equations

Graphing a linear equation involves plotting points that satisfy the equation on a Cartesian plane. To graph x - 4y = 8, one can rearrange it into slope-intercept form (y = mx + b) or find intercepts. The slope indicates the steepness of the line, while the y-intercept shows where the line crosses the y-axis.

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. This form is useful for quickly identifying the line's steepness and where it intersects the y-axis. Converting the given equation into this form can simplify the graphing process.