11. Graph the equation \( -3 x+y=1 \) Alope \( = \) -interospt =

To graph the equation \( -3x + y = 1 \), you can first rearrange it into slope-intercept form \( y = mx + b \). Adding \( 3x \) to both sides gives \( y = 3x + 1 \). Here, the slope (\( m \)) is 3, meaning for every one unit you move right on the x-axis, you go up three units on the y-axis. The y-intercept (\( b \)) is 1, putting it at the point (0,1) on the graph. Now, let’s take a quick detour into the world of intersest intercepts! The points where the line crosses the axes are important. For this equation, the y-intercept occurs when \( x = 0 \) which gives us (0, 1). For the x-intercept, set \( y = 0 \): \( -3x + 0 = 1 \) leads to \( x = -\frac{1}{3} \), giving the point \((- \frac{1}{3}, 0)\). Plotting these points will help you sketch the line beautifully!