Question

3. Match the equation with its graph.-7/6x - 3/7y= 1/2

Answer 1

Given the equation below

`(-7)/(6)x-(3)/(7)y=(1)/(2)`

The graph of the line equation above, first let us find the intercept on the y-axis, then intercept on the x-axis as shown below:

`\begin{gathered} i\text{ntercept on the y-axis, make x=0} \\ (-7)/(6)(0)-(3)/(7)y=(1)/(2) \\ -(3)/(7)y=(1)/(2) \\ -(7)/(3)*-(3)/(7)y=-(7)/(3)*(1)/(2) \\ y=(7)/(6) \\ y=1.167, \\ y-\text{intercept coordinate is }(0,1.167) \end{gathered}`
`\begin{gathered} \text{intercept on the x-axis, make y=0} \\ (-7)/(6)x-(3)/(7)(0)=(1)/(2) \\ -(7)/(6)x=(1)/(2) \\ -(6)/(7)*-(7)/(6)x=-(6)/(7)*(1)/(2) \\ x=-(6)/(14) \\ x=-0.429 \\ x-\text{intercept coordinate is (-0.429, 0)} \end{gathered}`

Plotting the x-intercept and y-intercept coordinates on a graph would give the graph below

From observation of the above straight line graph, the option that has the same pattern is the third option

Hence, the correct option is OPTION 3