Question

Write the equation in slope-intercept form. Then graph the equation. $$ 5 x-y=4 $$

Short answer

The slope-intercept form of the equation is \( y = 5x - 4 \) with slope 5 and y-intercept -4. Start the graph by marking the y-intercept at -4, then move up 5 units for each 1 move right along the x-axis. Connect the points with a straight line.

Step-by-step solution

Convert to Slope-Intercept Form

Our given equation is \(5x - y = 4\). Firstly, to make y the subject, add \(y\) in both sides so the equation becomes \(5x - 4 = y\). This is the slope-intercept form where the slope \(m=5\), and y-intercept \(c=-4\).

Identify the Slope and Intercept

From the slope-intercept form, it can be seen that the slope \(m=5\), which indicates that for each step along the x-axis, one moves 5 steps up along the y-axis. The intercept \(c=-4\) signifies that the line crosses the y-axis at -4.

Graph the Equation

Draw a 2-dimensional graph. Begin by marking the y-intercept at -4 on the y-axis. Then, use the slope to locate next points by moving 1 step to the right on the x-axis and 5 steps up for the y-axis. Plot these points and connect them with a straight line. The line represents the equation in slope-intercept form.