Final answer:
To find the equation in slope-intercept form for the line that is perpendicular to y = -x + 9 and passes through the point (-3, 2), we need to determine the slope and the y-intercept of the line. The slope of the perpendicular line is the negative reciprocal of the slope of the original line, and we use the coordinates of the given point to find the value of the y-intercept. Lastly, we write the equation in slope-intercept form using the known values.
Step-by-step explanation:
To write an equation in slope-intercept form for the line that is perpendicular to y = -x + 9 and passes through the point (-3, 2), we need to determine the value of the slope. The slope of the original line is -1, so the slope of the perpendicular line will be the negative reciprocal of -1, which is 1. Therefore, the equation for the perpendicular line can be written as y = 1x + b. Next, we substitute the coordinates of the given point (-3, 2) into the equation to find the value of b. We get 2 = 1(-3) + b. Simplifying this equation gives b = 5. Thus, the equation in slope-intercept form for the line that passes through (-3, 2) and is perpendicular to y = -x + 9 is y = x + 5.