Step-by-step explanation:
the general line equation format is
y = ax + b
a is the slope or gradient of the line. it is the ratio of "y coordinate change / x coordinate change".
b is the y-intercept, the y value when x = 0. we get this by putting one point into the equation and solve for b.
(i)
A (3, 5)
B (5, 9)
x changes by +2 (from 3 to 5).
y changes by +4 (from 5 to 9).
so, the slope (or gradient) is +4/+2 = 2
(ii)
the semi-finished equation is
y = 2x + b
let's use A to get b :
5 = 2×3 + b = 6 + b
b = -1
and the full equation is
y = 2x - 1
(iii)
for point (4, k) we get
k = 2×4 - 1 = 8 - 1 = 7
