Question

Perpendicular to y=2x+9 and has the point (4,-1)

Answer 1

Answer:

$\sf y=-\dfrac{1}{2}x+1$

Step-by-step explanation:

Slope-intercept form: y = mx + b

where:

• m is the slope
• b is the y-intercept (when x = 0)

Given: y = 2x + 9

where:

• 2 is the slope
• (0, 9) is the y-intercept

Note:

Perpendicular lines have slopes that are negative reciprocals of each other. 

$\sf \textsf{a slope of 2} \implies \textsf{would have a negative reciprocal of} -\dfrac{1}{2}$

$\textsf{Perpendicular line:}\ \sf y=-\dfrac{1}{2}x+b$

Substitute the given point into the the equation to find the value of b:

$\sf \sf y=-\dfrac{1}{2}x+1\\\\-1=-\dfrac{1}{2}(4)+b\\\\-1=-2+b\\\\-1+2=-2+2+b\\\\1=b$

$\textsf{Perpendicular line:}\ \sf y=-\dfrac{1}{2}x+1$

• slope of ½
• y-intercept of (0, 1)

Answer 2

Answer: y =  $-\frac{1}{2}$x + 1

Step-by-step explanation:

      First, we will find the slope. The slope of perpendicular lines are negative reciprocals.

      In this case, the first slope is 2. The negative of 2 is -2, and the reciprocal of -2 is $-\frac{1}{2}$.

      Now, we will plug in this new slope, the point given, and solve for the b, or the y-intercept.

y = mx + b

(-1) =  ($-\frac{1}{2}$)(4) + b

-1 =  -2 + b

1 = b

     Lastly, we will write our equation.

y = mx + b

y =  $-\frac{1}{2}$x + 1

          The line is y =  $-\frac{1}{2}$x + 1, or y = 1 - $\frac{x}{2}$.