The slope-intercept form of a line is y equals m x plus b. Here, m represents the slope and b represents the y-intercept. For our line, the slope m is three-halves and the y-intercept b is negative two. So our equation is y equals three-halves x minus two.
The y-intercept is the point where the line crosses the y-axis. This happens when x equals zero. Substituting x equals zero into our equation: y equals three-halves times zero minus two, which equals negative two. So the y-intercept point is (0, negative 2).
The slope tells us how the line changes. It's the ratio of vertical change to horizontal change, often described as 'rise over run'. For our slope of three-halves, this means a rise of 3 units for every run of 2 units. Starting from our y-intercept point (0, negative 2), we move right 2 units and then up 3 units to reach the point (2, 1).
We can find more points by continuing the slope pattern. From our point (2, 1), we move right 2 units and up 3 units to reach (4, 4). We can also move in the opposite direction. From our y-intercept (0, negative 2), we move left 2 units and down 3 units to reach the point (negative 2, negative 5). Now we have four points on our line.
Now we connect all our points to form the complete line. First, we plotted the y-intercept point (0, negative 2). Then, we used the slope of three-halves to find additional points: (negative 2, negative 5), (2, 1), and (4, 4). Finally, we drew a straight line through all these points, extending it infinitely in both directions with arrows to show it continues forever.
Let's verify our line by checking if points satisfy the equation. For point (2, 1): substituting x equals 2 into our equation gives y equals three-halves times 2 minus 2, which equals 3 minus 2, or 1. This matches our point! For point (negative 2, negative 5): substituting x equals negative 2 gives y equals three-halves times negative 2 minus 2, which equals negative 3 minus 2, or negative 5. This also matches! Both points satisfy the equation, confirming our graph is correct.