1. To find for the linear function from this problem, we use the formula:
x/a + y/b = 1
where a is the x intercept and b is the y intercept
x/-9 + y/3 = 1
Multiply everything by -9:
x – 3y = -9
Rearranging:
3y = x + 9
y = (1/3) x + 3
2. The general form of a linear function is:
y = mx + b
where m is the slope and b is the y-intercept
y = (-2/5) x + b
when y = 0, x = 1 therefore the b is:
0 = -2/5 + b
b = 2/5
y = (-2/5) x + 2/5
3. We create two equations from the general form y = mx + b or f(x) = mx + b
-5 = (1/6) m + b
-10 = (1/2) m + b
Subtract the two equations:
-5 - -10 = (1/6 – ½) m
5 = -1/3 m
m = -15
y = -15x + b
using any pair to get the value of b:
-5 = -15 (1/6) + b
b = -2.5
y = -15x – 2.5
4. same steps with number 3
-2/3 = (1) m + b
2 = (2/3) m + b
Subtract the two equations:
-2/3 - 2 = (1 – 2/3) m
-8/3 = 1/3 m
m = -8
y = -8x + b
using any pair to get the value of b:
2 = -8(2/3) + b
b = 22/3
y = -8x + 22/3
5. From the graph we have the points:
(-5, 4) and (4, -4)
So we create two equations:
4 = (-5) m + b
-4 = (4) m + b
Subtract the two equations:
4 - -4 = (-5 - 4) m
8 = -9 m
m = -8/9
y = (-8/9) x + b
using any pair to get the value of b:
4 = (-8/9) (-5) + b
b = -4/9
y = (-8/9) x – 4/9
6. From the graph we have the points:
(2, -5) and (4, 6)
So we create two equations:
-5 = (2) m + b
6 = (4) m + b
Subtract the two equations:
-5 - 6 = (2 - 4) m
-11 = -2 m
m = 5.5
y = 5.5 x + b
using any pair to get the value of b:
-5 = 5.5 (2) + b
b = -16
y = 5.5 x – 16
7. We can actually solve this easily by plotting the points. We can see that by plotting the points, a curve line is created, not a straight one.
<check the graph photo attached>
8. Let us say that the x intercept, a = 1 and the y intercept, b = 1. Prove that slope m = -1
From the equation:
x/a + y/b = 1
x/1 + y/1 = 1
x + y = 1
y = -x + 1
Hence slope is m = -1