Final answer:
To find the equation of a line perpendicular to y=3/4x+2 that runs through the point (3,-2) in slope-intercept form, we need to determine the slope of the new line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
Step-by-step explanation:
To find the equation of a line perpendicular to y=3/4x+2 that runs through the point (3,-2) in slope-intercept form, we need to determine the slope of the new line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The original line has a slope of 3/4, so the perpendicular line will have a slope of -4/3.
Using the point-slope form of a line, we can substitute the slope and the given point into the equation y-y1=m(x-x1) to find the equation of the perpendicular line. Substituting (x1,y1)=(3,-2) and m=-4/3, we get the equation y-(-2)=(-4/3)(x-3).
Simplifying, we get the equation y+2=(-4/3)x+4. By rearranging the equation to slope-intercept form, we obtain the equation of the line perpendicular to y=3/4x+2 as y=(-4/3)x+2.