Final answer:
To find the equation of the line that contains the points (2, -3) and (-2, 6), we need to find the slope (m) using the formula (change in y)/(change in x). Then, substitute one of the given points into the equation to find the y-intercept (b). Finally, convert the equation from slope-intercept form to standard form by rearranging the terms.
Step-by-step explanation:
To find the equation of the line that contains the points (2, -3) and (-2, 6), we can use the slope-intercept form of a linear equation, which is y = mx + b. First, we need to find the slope (m) using the formula (change in y)/(change in x). The change in y is 6 - (-3) = 9, and the change in x is -2 - 2 = -4. Therefore, the slope is m = 9/-4 = -9/4. Now, we can choose one of the given options that has the correct slope and substitute one of the given points into the equation to find the y-intercept (b).
Option 1: y = 3x - 9, substitute the point (2, -3): -3 = 3(2) - 9 = -3. This option is correct.
Finally, we can convert the equation from slope-intercept form to standard form by rearranging the terms. Option 1: y = 3x - 9 is equivalent to 3x - y = 9. Therefore, the correct answer is Option 1: y = 3x - 9, standard form: 3x - y = 9.