Explanation:
1a.
I assume the equation is meant to be in slope/ intercept form.
that means it will look like
y = ax + b
"a" being the slope, b being the y-intercept (the y value when x = 0).
the slope is the ratio (y coordinate change / x coordinate change) when going from 1 point on the line to another point on the line.
so, we know
y = 2.5x + b
b we get by using the point coordinates in the equation :
54 = 2.5×20 + b = 50 + b
4 = b
so, the full equation is
y = 2.5x + 4
1b.
my favorite point is always x = 0
y = 2.5×0 + 4 = 4
so, another point is e.g. (0, 4).
2.
x^-4
e.g. x²/x⁶, x²×x^-6, x²×x²/x⁸
I know that all of them are equivalent to x^-4, because when multiplying variable factors, the exponents are added for the new exponent and when divided, the exponents are subtracted for the new exponent.
3a is i.
the graph in i. is the only one with a negative slope (the line goes down when moving left to right).
3c is ii.
the slope shows that x has to increase by 4 to increase y by 1.
given the scale it is easier to check an increase in x by 8 that leads to an increase in y by 2.
the ratio 2/8 = 1/4.
3d is most likely iii.
I cannot see the scaling of the x-axis. so, I can only suspect what is going on.
the score of 1/2 of the line indicates that x changes by 2 to increase y by 1. or under the same ratio, x changes by 4, y changes by 2. or x changes by 8, y changes by 4 (and I think that is what iii. is).
that leaves us with 3b. is iv.
it means that for a change of 1 in x, we have a change in y by 2.
again I cannot see the scaling of x, so I can only suspect here too.