a)using intercepts, graph the three lines 4x + y - 8=0, 2x - y - 4=0, x + 2y - 16 = 0
To graph the three lines using intercepts, we need to find the x and y-intercepts of each line.
a) For the line 4x + y - 8 = 0:
To find the x-intercept, set y = 0 and solve the equation for x:
4x + 0 - 8 = 0
4x = 8
x = 2
So the x-intercept is (2, 0).
To find the y-intercept, set x = 0 and solve the equation for y:
4(0) + y - 8 = 0
y - 8 = 0
y = 8
So the y-intercept is (0, 8).
Now we have two points on the line: (2, 0) and (0, 8). Plot these two points on a graph and draw a line passing through them.
b) For the line 2x - y - 4 = 0:
To find the x-intercept, set y = 0 and solve the equation for x:
2x - 0 - 4 = 0
2x = 4
x = 2
So the x-intercept is (2, 0).
To find the y-intercept, set x = 0 and solve the equation for y:
2(0) - y - 4 = 0
-y - 4 = 0
y = -4
So the y-intercept is (0, -4).
Now we have two points on the line: (2, 0) and (0, -4). Plot these two points on the same graph and draw a line passing through them.
c) For the line x + 2y - 16 = 0:
To find the x-intercept, set y = 0 and solve the equation for x:
x + 2(0) - 16 = 0
x - 16 = 0
x = 16
So the x-intercept is (16, 0).
To find the y-intercept, set x = 0 and solve the equation for y:
0 + 2y - 16 = 0
2y = 16
y = 8
So the y-intercept is (0, 8).
Now we have two points on the line: (16, 0) and (0, 8). Plot these two points on the same graph and draw a line passing through them.
After graphing all three lines, you should have a visual representation of their intersection points, if any.