Ok, so
First of all, remember that a line can be described by two forms:
1. y = mx+b, where m is the slope and b is the y - intercept-
2. We would have the general equation for a line, which is:
Ax + By + C = 0
Where m(slope) is -A/B and the intercept (b) is -C/B.
Now, let's find the slope and y - intercept for each line here below.
a. y = 5 - 6x
Here we have a line which has the first form (1). So, if we rewrite:
y = - 6x + 5.
So, If we compare with the first equation, we notice that m = -6 and b = 5
or, m = -6 and b = (0,5)
b. y = (5/6)x + 1
Here we have a line which has the first form (1).
So, if we compare, we notice that m = 5/6 and b = 1, or, m = 5/6 and b = (0,1)
c. 5x - 6y = 6
If we rewrite the equation:
5x - 6y - 6 = 0
Here we have a line which has the second form (2).
We know that
A = 5
B = -6
C = -6
If we replace, m = -A/B, which is -(5) / (-6) , and this is 5/6.
And, y intercept will occurs at y = -C/B, which is -(-6) / -6, which is 6/-6, or -1.
So, the slope will be 5/6 and y-intercept (0,-1).
m = 5/6 and b = (0,-1)
d. 5x + 6y = 6
If we rewrite the equation:
5x + 6y - 6 = 0
Here we have a line which has the second form (2).
We know that:
A = 5
B = 6
C = -6
If we replace, m = -A/B, which is -(5) / 6, so, m = -5/6
And, y intercept will occurs at y = -C/B, which is -(-6) / 6, so, b = 1
Finally, m = -5/6, and b = (0,1)