Graph each equation.
$x-4y=8$

Verified step by step guidance

1. Rewrite the given equation \(x - 4y = 8\) in slope-intercept form \(y = mx + b\) by isolating \(y\) on one side. Start by subtracting \(x\) from both sides: \(-4y = -x + 8\).
2. Next, divide every term by \(-4\) to solve for \(y\): \(y = \frac{-x}{-4} + \frac{8}{-4}\).
3. Simplify the fractions to get the slope-intercept form: \(y = \frac{1}{4}x - 2\).
4. Identify the slope \(m = \frac{1}{4}\) and the y-intercept \(b = -2\). This means the line crosses the y-axis at \((0, -2)\) and rises 1 unit for every 4 units it moves to the right.
5. Plot the y-intercept on the graph, then use the slope to find another point by moving right 4 units and up 1 unit. Draw a straight line through these points to graph the equation.

Key Concepts

Linear Equations in Two Variables

A linear equation in two variables, like x - 4y = 8, represents a straight line on the coordinate plane. Each solution (x, y) satisfies the equation, and the graph is the set of all such points. Understanding this helps in visualizing and plotting the line.

Slope-Intercept Form

Rearranging the equation into slope-intercept form (y = mx + b) makes graphing easier by identifying the slope (m) and y-intercept (b). For example, solving x - 4y = 8 for y gives y = (1/4)x - 2, showing the line’s steepness and where it crosses the y-axis.

Plotting Points and Drawing the Line

To graph the equation, plot the y-intercept on the coordinate plane, then use the slope to find another point by rising and running from the intercept. Connecting these points with a straight line represents all solutions to the equation.