Question

Graphs and equations of lines

Answer 1

a)
`y = -(3)/(4) x + 5`

b)
`y = 6x-18`

c)
`y = (4)/(5) x+(19)/(5)`

Explanation:

a) The slope / gradient is the coefficient of
`x`, so for a) it will be
`y=-(3)/(4) x + C`.

C is the y-intercept, so the full equation will be
`y = -(3)/(4) x + 5`.

b) Again, since the slope is 6, we know the coefficient of
`x` will be 6.

Now, we have a point on the line and so far, we know the equation is
`y=6x+c`. The coordinates of the point are (2,-6). So now we substitute the y and x values into the equation in order to find C.

`-6 = 6(2)+C`

`-6 = 12+C`

`C = -18`

`y = 6x-18`

c) To find the gradient we must use the formula
`(rise)/(run)`.

rise = change in y value

run = change in x value

so, the gradient
`= (7-3)/(4-(-1)) = (4)/(5)`

Now the equation is
`y = (4)/(5) x +C`

Again, to find C we substitute any of the coordinates into the equation. I will use (-1,3).

`3 = (4)/(5) (-1) +C`

`3 + (4)/(5) =C`

`C =(19)/(5)`

so c) is
`y = (4)/(5) x+(19)/(5)`