Question

Line k is graphed on a coordinate plane. The equation y = 3 4 x − 1 y = 3 4 x − 1 describes line k. Line m contains the point ( 1 , 6 ) ( 1 , 6 ) and is perpendicular to line k. Which of these equations describes line m?

Answer 1

The equation for line m, perpendicular to line k and passing through the point (1, 6), is y=− 4/3x+ 22/3.

To find the equation for line m perpendicular to line k and passing through the point (1, 6), it's crucial to understand the relationship between the slopes of perpendicular lines. The given equation for line k is y= 3/4x−1, indicating that its slope is 3/4.

For a line perpendicular to k, the negative reciprocal of 3/4 is taken as the slope. The negative reciprocal is −4/3. Now, we have the slope for line m. To determine the equation, the point-slope form y−y1​=m(x−x1​) is employed, where (x1​,y1​) is the given point (1, 6) and m is the slope.

Substituting in the values, we get y−6=− 4/3(x−1). Simplifying this equation yields y=− 4/3​x+ 22/3, which is the equation for line m. This ensures that line m is perpendicular to line k and passes through the specified point (1, 6).

Complete ques:

Determine the equation for line m which is perpendicular to line k and contains the point (1, 6), given that line k is represented by the equation y= 3/4x−1.