Answer:
-3/4
Explanation:
The slope of a line is a measure of its steepness and direction, and it is defined as the change in y divided by the change in x for any two points on the line. If a line is perpendicular to another line, it means that the two lines are at a 90 degree angle to each other. The slope of a line that is perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line.
To find the slope of the original line, we can rewrite the equation 3y = -4x + 2 in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, we can divide both sides of the equation by 3 to obtain:
y = (-4/3)x + 2/3
The slope of the original line is therefore (-4/3). To find the slope of a line that is perpendicular to this line, we can take the negative reciprocal of (-4/3), which is 3/-4 = -3/4.
Therefore, the slope of a line that is perpendicular to the line whose equation is 3y = -4x + 2 is -3/4.