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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