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Draw a graph of the line that contains the given point and has the given slope. (0,6),m=-1

Draw a graph of the line that contains the given point and has the given slope.\newline(0,6),m=−1 (0,6), m=-1

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Full solution

Q. Draw a graph of the line that contains the given point and has the given slope.\newline(0,6),m=−1 (0,6), m=-1
  1. Identify y-intercept and slope: Identify the y-intercept and slope from the given information. The point (0,6)(0,6) indicates that the y-intercept is 66. The slope mm is given as −1-1.
  2. Use slope-intercept form: Use the slope-intercept form of a line equation, y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Plugging in the values, we get y=−1x+6y = -1x + 6.
  3. Simplify the equation: Simplify the equation to y=−x+6y = -x + 6. This is the equation of the line.
  4. Graph the line: To graph this line, start at the y-intercept (0,6)(0,6) on the y-axis. From this point, since the slope is −1-1, move down 11 unit and right 11 unit to find another point on the line, which is (1,5)(1,5).
  5. Plot points and draw line: Plot the points (0,6)(0,6) and (1,5)(1,5) on a graph. Draw a straight line through these points to represent the line y=−x+6y = -x + 6.

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