Question

the equation of a line is given below. \\( 3x + y = 1 \\) find the slope and the \\( y \\)-intercept. then use them to graph the line.

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.
We are given the equation $3x + y=1$.
Subtract $3x$ from both sides of the equation: $y=-3x + 1$.

Step2: Identify the slope and the y - intercept

From the equation $y=-3x + 1$, comparing with $y = mx + b$, we can see that the slope $m=-3$ and the $y$ - intercept $b = 1$.

Step3: Find the x - intercept

To find the $x$ - intercept, we set $y = 0$ in the original equation $3x + y=1$.
Substitute $y = 0$ into the equation: $3x+0 = 1$.
Solve for $x$: $3x=1$, so $x=\frac{1}{3}$.

Answer:

Slope: $- 3$, $y$ - intercept: $1$, $x$ - intercept: $\frac{1}{3}$