Determine whether the equation is linear or not. Then graph the equation by finding and plotting ordered-pair solutions. \( 4 x-y=4 \)

To determine whether the equation \( 4x - y = 4 \) is linear, we can look at the highest power of the variable. In this case, the highest power of \( x \) is 1, and the highest power of \( y \) is 1. Since there are no terms with powers higher than 1, the equation is linear. Now, let's graph the equation by finding and plotting ordered-pair solutions. First, we can rearrange the equation to solve for \( y \) in terms of \( x \): \( 4x - y = 4 \) \( -y = -4x + 4 \) \( y = 4x - 4 \) Now we have the equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In this case, the slope \( m \) is 4 and the y-intercept \( b \) is -4. To graph the equation, we can plot the y-intercept first. The y-intercept is the point where the line crosses the y-axis, and it is given by the value of \( b \). So, the y-intercept is (0, -4). Next, we can use the slope to find another point on the line. The slope tells us how much \( y \) changes for every unit change in \( x \). Since the slope is 4, for every 1 unit we move to the right on the x-axis, we move up 4 units on the y-axis. Starting from the y-intercept (0, -4), we move 1 unit to the right (to x = 1) and 4 units up (to y = 0). This gives us the point (1, 0). Now we have two points on the line: (0, -4) and (1, 0). We can plot these points on a coordinate plane and draw a straight line through them to graph the equation. Here's a visual representation of the graph: ``` y | | * | / | / | / | / | / | / |/ -----------------x 0 1 ``` The line shown above represents the graph of the equation \( 4x - y = 4 \).