Question

graph the line with slope 3 passing through the point (-3, 3).

Explanation:

Step1: Plot the given point

Locate the point \((-3, 3)\) on the coordinate plane. The \(x\)-coordinate is \(-3\) (3 units to the left of the origin on the \(x\)-axis) and the \(y\)-coordinate is \(3\) (3 units up from the origin on the \(y\)-axis). Mark this point.

Step2: Use the slope to find another point

The slope \(m = 3\) can be written as \(\frac{3}{1}\), which means for every \(1\) unit we move to the right (increase in \(x\) by \(1\)), we move up \(3\) units (increase in \(y\) by \(3\)). Starting from \((-3, 3)\), move \(1\) unit to the right (to \(x=-3 + 1=-2\)) and \(3\) units up (to \(y = 3+3 = 6\)). So the new point is \((-2, 6)\). We can also move in the opposite direction: for a slope of \(\frac{3}{1}\), the negative slope would be \(\frac{-3}{-1}\), so moving \(1\) unit to the left (decrease \(x\) by \(1\)) and \(3\) units down (decrease \(y\) by \(3\)) from \((-3, 3)\) gives \((-4, 0)\).

Step3: Draw the line

Connect the points (e.g., \((-3, 3)\), \((-2, 6)\), \((-4, 0)\)) with a straight line and extend it in both directions. The line should pass through these points and have a positive slope (going up from left to right) with a steepness corresponding to a slope of \(3\).

(Note: Since the problem is about graphing, the final answer is the graph as described, but in the context of the solution, we've outlined the steps to draw it.)

Answer:

The line is graphed by plotting \((-3, 3)\), using the slope \(3\) to find other points (e.g., \((-2, 6)\), \((-4, 0)\)), and drawing a straight line through them.