Question

find the slope and y - intercept
y = -\frac{1}{3}x + 3 \quad slope \\_\\_\\_\\_ y - intercept \\_\\_\\_\\_
y = 2x - 3 \quad \quad \quad slope \\_\\_\\_\\_ y - intercept \\_\\_\\_\\_
y = -2x - 6 \quad \quad slope \\_\\_\\_\\_ y - intercept \\_\\_\\_\\_
\quad \quad \quad \quad \quad \quad slope \\_\\_\\_\\_ y - intercept

Explanation:

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

For $y=-\frac{1}{3}x + 3$:

Step 1: Identify the slope

In the equation $y=-\frac{1}{3}x + 3$, comparing with $y = mx + b$, the coefficient of $x$ (i.e., $m$) is $-\frac{1}{3}$. So the slope is $-\frac{1}{3}$.

Step 2: Identify the y - intercept

In the equation $y=-\frac{1}{3}x + 3$, comparing with $y = mx + b$, the constant term $b$ is $3$. So the y - intercept is $3$.

For $y = 2x-3$:

Step 1: Identify the slope

In the equation $y = 2x-3$, comparing with $y = mx + b$, the coefficient of $x$ (i.e., $m$) is $2$. So the slope is $2$.

Step 2: Identify the y - intercept

In the equation $y = 2x-3$, comparing with $y = mx + b$, the constant term $b$ is $- 3$. So the y - intercept is $-3$.

For $y=-2x - 6$:

Step 1: Identify the slope

In the equation $y=-2x - 6$, comparing with $y = mx + b$, the coefficient of $x$ (i.e., $m$) is $-2$. So the slope is $-2$.

Step 2: Identify the y - intercept

In the equation $y=-2x - 6$, comparing with $y = mx + b$, the constant term $b$ is $-6$. So the y - intercept is $-6$.

Answer:

s:

• For $y =-\frac{1}{3}x + 3$: Slope is $-\frac{1}{3}$, y - intercept is $3$.
• For $y=2x - 3$: Slope is $2$, y - intercept is $-3$.
• For $y=-2x - 6$: Slope is $-2$, y - intercept is $-6$.