Question

A (-2,y) B (4,-6), gradient: -1/6
Find y using the cross-multiply method

Answer 1

Key Ideas

• Finding a coordinate point given the gradient/slope
• Cross multiplication
• Slope equation

We use the slope equation to solve for the slope/gradient of a line:

`m=(y_2-y_1)/(x_2-x_1)`

• m = the slope
• 
  `(x_1,y_1)` and
  `(x_2,y_2)` are two points that fall on the line

Solving the Question

We're given:

• A (-2,y)
• B (4,-6)
• Gradient =
  `-(1)/(6)`

`m=(y_2-y_1)/(x_2-x_1)`

Plug in the given information:

`-(1)/(6)=(-6-y)/(4-(-2))\\\\-(1)/(6)=(-6-y)/(4+2)\\\\-(1)/(6)=(-6-y)/(6)`

Cross multiply (by multiplying the numerators by the opposite denominators):

`-(1)/(6)=(-6-y)/(6)\\\\-1* 6=6(-6-y)\\-6=-36-6y\\30=-6y\\y=-5`

Answer

y = -5