Questions: The equation of a line is given below. 2 x+y=1 Find the slope and the y-intercept. Then use them to graph the line.

Transcript text: The equation of a line is given below. \[ 2 x+y=1 \] Find the slope and the $y$-intercept. Then use them to graph the line.

Solution

Solution Steps

Step 1: Rewrite the Equation in Slope-Intercept Form

To find the slope and the $y$-intercept, we need to rewrite the equation in the slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

Starting with the given equation: \[ 2x + y = 1 \]

Subtract $2x$ from both sides: \[ y = -2x + 1 \]

Step 2: Identify the Slope and $y$-Intercept

From the equation $y = -2x + 1$, we can identify the slope $m$ and the $y$-intercept $b$.

The slope $m$ is $-2$.

The $y$-intercept $b$ is $1$.

Final Answer

The slope of the line is $-2$ and the $y$-intercept is $1$.

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 5}, "commands": ["y = -2x + 1"], "latex_expressions": ["$y = -2x + 1$"]}

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