Find the slope and Y intercept of the line 3x + y 9 = 0

To find the slope and $Y$-intercept of the line given by the equation $3x+y-9=0$, we must first rewrite the equation in the slope-intercept form of a line, which is:

$$y=mx+b$$

where:

• $m$ is the slope of the line,
• $b$ is the $Y$-intercept (the value of $y$ when $x=0$).

Step 1: Rewrite the equation in slope-intercept form

Starting with the given equation:

$$3x+y-9=0$$

We isolate $y$ on one side:

$$y=-3x+9$$

Here, we moved $3x$ and $9$ to the other side of the equation, changing their signs accordingly.

Step 2: Identify the slope ($m$) and $Y$-intercept ($b$)

From the rewritten equation:

$$y=-3x+9$$

• The slope ($m$) is the coefficient of $x$, which is -3.
• The $Y$-intercept ($b$) is the constant term on the right-hand side, which is 9.

Verification

To ensure correctness, let's verify by plugging $x=0$ into the original equation:

$$3(0)+y-9=0⟹y=9$$

This confirms that the $Y$-intercept is indeed 9.

Final Answer

• Slope ($m$): -3
• $Y$-intercept ($b$): 9