Answer: Hi!
If you have a function y(x) = ax + b, where the slope is the number a and b is the x-axis intercept, whe can find the slope in the next way
where x2 and x1 are different numbers.
now we know that our line passes through the points:
A) (1, 9) and (3, 19) (where the notation stands for (x, y))
we can find the slope as
then the slope of this line is equal to 5, and we now need to finde the intercept b.
y(x) = 5x + b
we can repalace one of the pairs in the equation and then find b. for example the pair (1, 9)
9 = 5*1 + b
b = 9-5 = 4
then our line is: y = 5x + 4
B) (2, –14) and (4, –24)
The slope is
now we need to find the intercept, we do the same as before:
y = -5x + b
-14 = -5*2 + b
b = -14 + 10 = -4
then our equation is y = -5x - 4
C) (1, 1) and (3, 11)
We do the same procedure as before:
slope:
now for the intercept:
y = 5x + b
1 = 5*1 + b
b = 1 - 5 = -4
then our line is y = 5x - 4
D) (2, –6) and (4, –16)
The slope is
now we need to find the value of the intercept:
y = -5x + b
-6 = -5*2 + b
b = -6 + 10 = 4
then our line is y = -5x + 4