Question

16 sketch the graph of the line: $3x + y = -1$

Explanation:

Step1: Rewrite the equation in slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
Starting with the equation $3x + y=-1$, we solve for $y$:
Subtract $3x$ from both sides of the equation: $y=-3x - 1$

Step2: Identify the slope and y - intercept

For the equation $y=-3x - 1$, the slope $m=-3$ (which is negative, meaning the line should be decreasing from left to right) and the y - intercept $b = - 1$ (the line crosses the y - axis at $(0,-1)$).

Step3: Analyze the graphs

• For graph A: The line has a positive slope (it is increasing from left to right) and a y - intercept of $0$ (it crosses the y - axis at the origin), so it does not match our equation.
• For graph B: The line has a negative slope (decreasing from left to right) and if we check the y - intercept, when $x = 0$, from the equation $y=-3(0)-1=-1$, and the line in graph B appears to cross the y - axis near $(0, - 1)$ and has a negative slope, which matches the equation $y=-3x - 1$.

Answer:

B