Question

3x + y = -3

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 $3x + y=-3$, we solve for $y$:
Subtract $3x$ from both sides of the equation: $y=-3x - 3$.

Step2: Identify the y - intercept and slope

For the equation $y=-3x - 3$, the y - intercept $b=-3$, which means the line crosses the y - axis at the point $(0,-3)$.
The slope $m=-3=\frac{-3}{1}$, which means for every 1 unit we move to the right along the x - axis, we move down 3 units.

Step3: Plot the y - intercept and use the slope to find another point

• Plot the point $(0, - 3)$ on the y - axis.
• Using the slope, from the point $(0,-3)$, move 1 unit to the right (increase $x$ by 1) and 3 units down (decrease $y$ by 3). This gives us the point $(1,-6)$.
• We can also find the x - intercept by setting $y = 0$ in the original equation $3x+y=-3$.

Substitute $y = 0$: $3x+0=-3$, so $3x=-3$, and $x=-1$. So the x - intercept is $(-1,0)$.

• Now we can draw a straight line through the points $(0,-3)$ and $(-1,0)$ (or $(1,-6)$) to graph the equation $3x + y=-3$.

Answer:

To graph $3x + y=-3$ (or $y=-3x - 3$), plot the y - intercept $(0,-3)$ and the x - intercept $(-1,0)$ (or use the slope to find another point like $(1,-6)$) and draw a straight line through these points.