Question

1. 3x - 6y = -3

Explanation:

Step1: Rewrite the equation in slope - intercept form

We start with $3x - 6y=-3$. First, isolate $y$. Subtract $3x$ from both sides: $-6y=-3x - 3$. Then divide each term by $-6$: $y=\frac{1}{2}x+\frac{1}{2}$.

Step2: Find the y - intercept

The y - intercept occurs when $x = 0$. Substitute $x = 0$ into $y=\frac{1}{2}x+\frac{1}{2}$, we get $y=\frac{1}{2}(0)+\frac{1}{2}=\frac{1}{2}$. So the y - intercept is the point $(0,\frac{1}{2})$.

Step3: Find the x - intercept

The x - intercept occurs when $y = 0$. Substitute $y = 0$ into $y=\frac{1}{2}x+\frac{1}{2}$, then $0=\frac{1}{2}x+\frac{1}{2}$. Subtract $\frac{1}{2}$ from both sides: $-\frac{1}{2}=\frac{1}{2}x$. Multiply both sides by $2$ to solve for $x$, we get $x=-1$. So the x - intercept is the point $(-1,0)$.

Step4: Plot the points and draw the line

Plot the y - intercept $(0,\frac{1}{2})$ and the x - intercept $(-1,0)$ on the coordinate grid and draw a straight line through them.

Answer:

The graph of the line $y=\frac{1}{2}x+\frac{1}{2}$ with x - intercept $(-1,0)$ and y - intercept $(0,\frac{1}{2})$ is drawn on the given coordinate grid.