Re-arrange the equation 4y - 3x = 8 in the form y = mx + cy = 3/4x +2The gradient is 3/4
Now we need to work out the gradient of the 2nd line. Remember that when 2 lines are perpendicular the product of their gradients is -1. Let's call the gradient of the second line m.
3/4m = -1m = -4/3In the question we are told that the line passes through the point (0, 2). This means that the line crosses the y axis at +2.
So the equation of the line that is perpendicular to 4y - 3x = 8 is y = - 4/3x + 2
Finding the gradient of a line between two points
To find the gradient of a line we need to know how many it goes up, for every one across.
Example
Find the gradient of the line joining (1,3) to (4,9).
As we go from (1,3) to (4,9) the y value increases by 6, and the x value increases by 3. So the line goes 6 up for 3 across. So this line has a gradient of 6/3 = 2.
Use this technique to answer the following question:
QuestionLine A goes through the points (4, 9) and (1, 3). Find the perpendicular line through the point (2, 0).
