Answer: x-intercept = 1
Step-by-step explanation: To solve this problem, we need to remember that the y-intercept is the point where the line crosses the y-axis. So if our line has a y-intercept of 3, it crosses the y-axis up 3 units. So we start this problem by plotting the point (0,3) on y-axis and we can label that point A.
From there, our slope of -3 can be thought of as -3/1 so we go down 3 units and to the right 1 unit and we plot point B. Notice that point B happens to lie on the x-axis at (1,0) and it's important to understand that the x-intercept is the point where the line crosses the x-axis.
Since our line crosses the x-axis at the point (1,0), it as an x-intercept of 1. If you're given a y-intercept and a slope like you are in this problem, you won't always be able to determine the x-intercept but things work out nicely here because point B happens to lie on the x-axis.
I provided an image with the graph and my work as well.