Question

(8) x - 3y = 4

Explanation:

Step1: Rewrite the equation in slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
Starting with the equation $x-3y = 6$, we want to solve for $y$.
Subtract $x$ from both sides: $- 3y=-x + 6$.
Divide each term by $-3$: $y=\frac{1}{3}x-2$.

Step2: Find the y - intercept and plot it

The y - intercept $b=-2$. So, the line crosses the y - axis at the point $(0, - 2)$.

Step3: Find another point using the slope

The slope $m = \frac{1}{3}$, which means for every 3 units we move to the right (increase in $x$ by 3), we move up 1 unit (increase in $y$ by 1).
Starting from the y - intercept $(0,-2)$, if we move 3 units to the right (to $x = 3$) and 1 unit up, we get the point $(3,-2 + 1)=(3,-1)$.

Step4: Draw the line

Now that we have two points, $(0,-2)$ and $(3,-1)$, we can draw a straight line passing through these two points on the given coordinate grid.

Answer:

To graph $x - 3y=6$ (or $y=\frac{1}{3}x - 2$), plot the y - intercept $(0,-2)$ and the point $(3,-1)$ (found using the slope $\frac{1}{3}$), then draw a straight line through these points.