Question

A walking path across a park is represented by the equation y= -4x - 6 . A new path will be built perpendicular to this path. The path will intersect at the point (-4 , 10) . Identify the equation that represents the new path .

Answer 1

Answer: $y=\frac{1}{4}x+11$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the equation of the line $y= -4x - 6$, you can identify that the slope is:

$m=-4$

By definition, the slopes of perpendicular lines are negative reciprocals, then the slope of equation  of the line that represents the new path which will be built perpendicular to other path, is:

$m=\frac{1}{4}$

Knowing that the path will intersect at the point (-4 ,10), you  need to substitute the slope and this point into  $y=mx+b$ and solve for "b":

$10=\frac{1}{4}(-4)+b\\\\10+1=b\\\\b=11$

Therefore, the equation that represents the new path is:

 $y=\frac{1}{4}x+11$

Answer 2

Answer:

y=1/4 x +11

Step-by-step explanation:

So this is a word problem but it isn't too bad to figure what they want:  They are looking for a line that is perpendicular to y=-4x-6 and goes through (-4,10).

So we are looking for an equation whose slope is the opposite reciprocal of the given equation's slope.

The given equation has a slope of -4

The opposite reciprocal of -4 is 1/4 so that is the slope of our new line.

So we know our equation is in the form of y=1/4 x+b

Now we are given that this line should go through (-4,10) so plug it in to find b.

10=1/4 * (-4)+b

10=-1+b

11=b

So the equation is y=1/4 x+11