Final answer:
To graph the linear equation -x + 4y = 4, find and plot the x-intercept and the y-intercept. The x-intercept is (-4, 0) and the y-intercept is (0, 1).
Step-by-step explanation:
To graph the linear equation -x + 4y = 4 by finding and plotting its intercepts, we first need to solve for the x-intercept and the y-intercept. The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. To graph the linear equation -x + 4y = 4, find and plot the x-intercept and the y-intercept. The x-intercept is (-4, 0) and the y-intercept is (0, 1).
To find the x-intercept, we set y = 0 and solve for x: -x + 4(0) = 4. Simplifying the equation gives us -x = 4, and dividing both sides by -1 gives us x = -4. So the x-intercept is (-4, 0).
To find the y-intercept, we set x = 0 and solve for y: -0 + 4y = 4. Simplifying the equation gives us 4y = 4, and dividing both sides by 4 gives us y = 1. So the y-intercept is (0, 1).
Now we can plot these two intercepts on a graph and draw a line through them to represent the equation -x + 4y = 4.