Find equation of each line. write answer in slope intercept form.
The line parallel to -3x+2y=9 and contains the point (-2, 1).
To find the equation of a line parallel to another line, we need to determine the slope of the given line.
Given line: -3x + 2y = 9
Step 1: Convert the equation to slope-intercept form (y = mx + b) by isolating y on one side:
2y = 3x + 9
y = (3/2)x + 9/2
Step 2: Determine the slope of the given line. In slope-intercept form, the coefficient of x is the slope. The slope of the given line is (3/2).
Since the line we are looking for is parallel, it will have the same slope as the given line, which is (3/2).
Step 3: Use the point-slope form (y - y1 = m(x - x1)) to find the equation of the parallel line using the given point (-2, 1):
(y - 1) = (3/2)(x - (-2))
(y - 1) = (3/2)(x + 2)
Step 4: Convert the equation to slope-intercept form:
y - 1 = (3/2)x + 3
y = (3/2)x + 3 + 1
y = (3/2)x + 4
Therefore, the equation of the line parallel to -3x + 2y = 9 and containing the point (-2, 1) is y = (3/2)x + 4 in slope-intercept form.