Question

Find and graph the intercepts of the following linear equation: -3x -9y=-18

Answer 1

Given the linear equation,

`-3x-9y=-18\text{ ----\lparen1\rparen}`

To determine the y-intercept, we need to write it in the form y = mx + c

where m is the gradient and c is the y-intercept.

Adding, 3x to both sides of (1)

`\begin{gathered} \Rightarrow-3x+3x-9y=3x-18 \\ \\ \Rightarrow-9y=3x-18 \end{gathered}`

Dividing both sides by -9

`\begin{gathered} \Rightarrow y=-(3)/(9)x-(18)/(-9) \\ \\ \Rightarrow y=-(1)/(3)x+2 \end{gathered}`

Hence, the y-intercept is 2

To find the x intercept, we equate y = 0 and the find the value of x

`\begin{gathered} \Rightarrow0=-(1)/(3)x+2 \\ \\ \Rightarrow(1)/(3)x=2 \\ \\ \Rightarrow x=6 \end{gathered}`

Therefore, the x-intercept is 6.

Knowing the x and y intercept, we can proceed to graph the linear function.