How do you write an equation in slope intercept form given (-2, 3) and is parallel to 3x + 2y = 10?

Question

Genesis Allen · Accepted Answer

#y-3=-3/2(x+2)#

Things to Remember

A line with the general form: #color(white)("XXX")Ax+By=C#
has a slope of #color(white)("XXX")m=-A/B#
All parallel lines have the same slope.
The slope-point form for a line with slope #m# through a point #(a,b)# is
#color(white)("XXX")y-b=m(x-a)#
Therefore for this example

a. #3x+2y=10# has a slope of #m=-3/2#
b. All lines parallel to #3x+2y=10# have a slope of #m=-3/2#
c. The slope point form for a line with slope #m=-3/2# through the point #(-2,3)# is
#color(white)("XXX")y-3=-3/2(x+2)#

Jameson Allen · Answer

undefined First, find the slope of the given line. Then, using the point-slope form, substitute the given point and the slope to find the equation of the line in slope-intercept form.

1. Rearrange the equation of the given line to solve for $ y $ in terms of $ x $, giving $ y = -\frac{3}{2}x + 5 $.
2. Since the line we want is parallel, it will have the same slope, $ m = -\frac{3}{2} $.
3. Use the point-slope form $ y - y_1 = m(x - x_1) $, where $ (x_1, y_1) $ is the given point and $ m $ is the slope, to find the equation of the line. Substitute $ (-2, 3) $ for $ (x_1, y_1) $ and $ -\frac{3}{2} $ for $ m $.

The equation in slope-intercept form is $ y = -\frac{3}{2}x + 6 $.