Step-by-step explanation:
(i)
that is really simple. for each point go vertically and horizontally to the x and y axis and see at what numbers you hit the axis.
A is -2 on x and +3 on y. so, it's coordinates are (-2, 3).
B is (4, 6).
(ii)
the gradient is also called the slope. it describes the "tilt" of the line.
the gradient or slope is expressed as ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point to another.
from (-2, 3) to (4, 6) :
x changes by +6 units (from -2 to 4).
y changes by +3 units (from 3 to 6).
so, the gradient/slope = 3/6 = 1/2
(iii)
the general line equation is
y = ax + b
a is the gradient/slope and is always the factor of x.
b is the y-intercept (the y value when x = 0, meaning the point the line crosses the y-axis).
we have already the gradient or slope.
we get b either by reading that point from the chart (it looks like (0, 4)) or by using the coordinates of one of the known points as x and y values in the equation and solve for b. I just picked (4, 6) :
6 = (1/2)×4 + b = 2 + b
b = 4
hey, we were right before !
so, the full line equation is
y = (1/2)x + 4 or simple x/2 + 4
