1. The problem is to graph the linear equation $y=3x+1$. 2. The slope is $3$ and the y-intercept is $1$. This means the line crosses the y-axis at the point $(0,1)$ and rises 3 units for every 1 unit it runs to the right. 3. Plot the point $(0,1)$ on the graph. From there, for every 1 unit you move to the right, move up 3 units, and plot another point to form the line. 4. Draw a straight line through the points extending in both directions. 1. The problem is to graph the equation $y=x-2$. 2. The slope is $1$ and the y-intercept is $-2$. This means the line crosses the y-axis at $(0,-2)$ and rises 1 unit for every 1 unit it runs to the right. 3. Plot the point $(0,-2)$. From this point, move 1 unit right and 1 unit up to plot another point. 4. Draw a straight line through these points. 1. The problem is to graph $y=-4x+2$. 2. The slope is $-4$ and y-intercept is $2$. The line crosses the y-axis at $(0,2)$ and falls 4 units for every 1 unit it goes right. 3. Plot $(0,2)$ and from there move 1 unit right and 4 units down to plot the next point. 4. Draw the line through the points. 1. The problem is to graph $y=\frac{1}{2}x-3$. 2. The slope is $\frac{1}{2}$ and y-intercept is $-3$. The line crosses y-axis at $(0,-3)$ and rises 1 unit for every 2 units it runs right. 3. Plot $(0,-3)$. From there, move 2 units right and 1 unit up to plot the next point. 4. Draw a straight line through these points. 1. The problem is to graph $y=\frac{1}{3}x-1$. 2. The slope is $\frac{1}{3}$ and y-intercept is $-1$. The line crosses y-axis at $(0,-1)$ and rises 1 unit for every 3 units to the right. 3. Plot $(0,-1)$. From there, move 3 units right and 1 unit up to plot another point. 4. Draw the line through these points. Final answers are the graphs of the five given linear functions.