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

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

$$y=mx+b$$

where:

• $m$ is the slope of the line,
• $b$ is the $Y$-intercept.

Step 1: Rewrite the equation in slope-intercept form

Starting with the given equation:

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

We isolate $y$ on one side of the equation:

$$y=-3x+9$$

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

From the rewritten equation:

$$y=-3x+9$$

• The coefficient of $x$ is $-3$, which represents the slope of the line.
• The constant term $9$ represents the $Y$-intercept of the line.

Step 3: Interpretation

• Slope ($m$): $-3$ This means that for every unit increase in $x$, $y$ decreases by 3 units.

• $Y$-intercept ($b$): $9$ This means that the line crosses the $Y$-axis at the point $(0,9)$.

Final Answer:

The slope of the line is -3, and the $Y$-intercept is 9.