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Graph this line:

y+3=
–
3(x–4)
Click to select points on the graph.

1 answer

To graph the equation \( y + 3 = -3(x - 4) \), we first need to simplify it to the slope-intercept form (y = mx + b).

  1. Start with the original equation: \[ y + 3 = -3(x - 4) \]

  2. Distribute the \(-3\): \[ y + 3 = -3x + 12 \]

  3. Subtract \(3\) from both sides to isolate \(y\): \[ y = -3x + 9 \]

Now, the equation is in the slope-intercept form \(y = mx + b\), where the slope \(m = -3\) and the y-intercept \(b = 9\).

To graph the line:

  1. Plot the y-intercept: Start by plotting the point \((0, 9)\) on the y-axis.
  2. Use the slope: From the y-intercept point \((0, 9)\), use the slope \(-3\) (which means a rise of \(-3\) and a run of \(1\)). Move down \(3\) units and then to the right \(1\) unit to plot another point at \((1, 6)\).
  3. Draw the line: Connect the two points with a straight line and extend it in both directions.

You can continue this by using the slope to find more points, such as from \((1, 6)\) moving down \(3\) and right \(1\) again to \((2, 3)\), or going back in the opposite direction.

Thus, the line can be represented by the points:

  • (0, 9)
  • (1, 6)
  • (2, 3)
  • (3, 0)

Finally, draw the line through these points, and you have the graph of the equation.