EXPLANATION
Given the line:
(1) y= -3x + 4
(2) y = -3x + 1
We can see that the slope is equal to m=-3 in both lines.
We need to start at the y-intercept of the top line, 4. From there, we would go down 3 to reach the line again.
Next, we need to fuse the y-intercept of the bottom line (0,1) and go over 3 to reach the second line. Doing this, we would hit the top line at (0.9,1.3)
We can use these two points in the distance formula to find how far apart the lines are:
[tex]\text{distance}=\sqrt[]{(0.9-0)^2-(1.3-1)^2}[/tex]Subtracting terms:
[tex]\text{distance = }\sqrt[]{(0.9)^2-(0.3)^2}[/tex]Solving the powers:
[tex]\text{distance}=\sqrt[]{0.81-0.09}=\sqrt[]{0.72}=\frac{3\sqrt[]{2}}{5}\approx0.85\text{ units}[/tex]Attaching the graph:
So, the distance between the lines is equal to 0.85 units.
