Write an equation that models the line that passes through the points (4,6) and (-4,8)

Use the y-intercept formula: y=mx+b
Plug in one of the points for x and y
Using that, solve for either x or y

For this type of question we use the formula for gradient, which as we know from lower school is rise/run. Rise is the change in the y values, while run is the change in the x values, so we just subtract one set of values from the other like so:
-4 - 4 = -8
8 - 6 = 2
Therefore the gradient of the line is -8/2 which equals -4. Now using the formula y = mx + c as a base we can substitute in one of the given points to solve for c given that we have just determined m to be -4:
y = mx + c = -4x + c
6 = -4(4) + c
6 = -16 + c
22 = c
Therefore the equation of this line is:
y = -4x + 22