Final answer:
To graph the equations using the point-slope method, rearrange the equations and identify the slope and a point on the line. Plot the given point in yellow and use the slope to find another point. Connect the two points to graph the line.
Step-by-step explanation:
To graph equations using the point-slope method, we need to find the slope and a point on the line. Let's go through the process for each option:
A. y - 7 = 3(x + 2)
First, we rearrange the equation to y = 3x + 13. The slope is 3, and a point on the line is (-2, 7). Plot that point in yellow, and then use the slope to find another point. Start from (-2, 7) and go 1 unit to the right and 3 units up to get another point. Connect the two points to graph the line.
B. y + 4 = ½(x - 2)
Rearrange the equation to y = 0.5x + 2. The slope is 0.5, and a point on the line is (2, -4). Plot that point in yellow, and then use the slope to find another point. Start from (2, -4) and go 2 units to the right and 1 unit up to get another point. Connect the two points to graph the line.
C. y -2 = 3(x -2)
Rearrange the equation to y = 3x - 4. The slope is 3, and a point on the line is (2, -2). Plot that point in yellow, and then use the slope to find another point. Start from (2, -2) and go 1 unit to the right and 3 units up to get another point. Connect the two points to graph the line.
D. y - 1 = (1/3)(x + 1)
Rearrange the equation to y = (1/3)x + 4/3. The slope is 1/3, and a point on the line is (-1, 1). Plot that point in yellow, and then use the slope to find another point. Start from (-1, 1) and go 3 units to the right and 1 unit up to get another point. Connect the two points to graph the line.
E. y - 2 = (-1/2)(x - 5)
Rearrange the equation to y = -0.5x + 4.5. The slope is -0.5, and a point on the line is (5, 2). Plot that point in yellow, and then use the slope to find another point. Start from (5, 2) and go 2 units to the left and 1 unit up to get another point. Connect the two points to graph the line.