Questions: Graph the line with the equation (y=-x+6).

Transcript text: Graph the line with the equation $y=-x+6$.

Solution

Solution Steps

Step 1: Identify the y-intercept

The equation is in slope-intercept form, $y = mx + b$, where $b$ is the y-intercept. In this case, $b = 6$. So the y-intercept is at the point $(0, 6)$.

Step 2: Identify the slope

The slope, $m$, is the coefficient of the $x$ term. In this case, $m = -1$. This means for every 1 unit moved to the right along the x-axis, the line moves down 1 unit along the y-axis.

Step 3: Plot the line

Start by plotting the y-intercept $(0,6)$. Then, use the slope to find another point. Moving 1 unit to the right and 1 unit down from $(0,6)$ gives the point $(1,5)$. Plot this point. Draw a line through these two points and extend it across the graph.

Final Answer:

The graph of the line is determined by plotting the y-intercept $(0,6)$ and using the slope $-1$ to find another point, like $(1,5)$, and drawing a line through those points.

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