Question

Find the gradient and the intercepts on the x and y axes of the straight line with the equation 3y=4-½x

Answer 1

the Given

`3y=4-(1)/(2)x`

We are to find the gradient and the intercepts on the x and y axes

The general form of equation of a line is

`y=mx+c_{}`

Simplifying the given equation we have

Dividing through by 3

`y=(4)/(3)-(1)/(6)x`

That is

`y=-(1)/(6)x+(4)/(3)`

Comparing this equation with the general equation of a line we have

Gradient = -1/6

x-intercept is at y = 0

Therefore

`\begin{gathered} 0=-(1)/(6)x+(4)/(3) \\ (1)/(6)x=(4)/(3) \\ 3x=24 \\ x=8 \end{gathered}`

Therefore x-intercept is (8,0)

y-intercept is at x = 0

Therefore

`\begin{gathered} y=-(1)/(6)(0)+(4)/(3) \\ y=(4)/(3) \end{gathered}`

Therefore, y-intercept = (0,4/3)