Find the line that is perpendicular to y = -3/4 x + 2 and passes through (3,4).
The equation of a line passing through point (a,b) at gradient m is:
(y - b) = m (x - a)
You're given (a,b)=(3,4).
What is the gradient of the perpendicular?
To find a line that is perpendicular to another line, we first need to determine the slope of the original line. So, in the given equation y = -3/4x + 2, we can see that the slope of the line is -3/4.
For any two perpendicular lines, the product of their slopes is -1. To find the slope of the line perpendicular to y = -3/4x + 2, we can take the negative reciprocal of -3/4.
The negative reciprocal of -3/4 is 4/3. Therefore, our perpendicular line will have a slope of 4/3.
Now, we can use the point-slope form of a linear equation to find the equation of the line passing through (3,4) with a slope of 4/3.
The point-slope form of a linear equation is: y - y₁ = m(x - x₁), where (x₁, y₁) represent the coordinates of a point on the line, and m is the slope of the line.
Plugging in the values (x₁, y₁) = (3,4) and m = 4/3 into the equation, we get:
y - 4 = (4/3)(x - 3)
Simplifying, we have:
y - 4 = (4/3)x - 4
Now, we can isolate y by moving -4 to the right side:
y = (4/3)x - 4 + 4
Simplifying further, we have:
y = (4/3)x
Therefore, the line perpendicular to y = -3/4x + 2 and passing through (3,4) is given by the equation y = (4/3)x.