please assist with steps

Question

Find an equation of the line that passes through the point (2,-7) and is perpendicular to the line 4x=y-8

Answer 1

Hi Sammy - 

 

The thing to keep in mind here is that the slopes of two perpendicular lines are the negative reciprocals of each other.

For example, for a line with a slope of 2, the slope of the line perpendicular to it would be -1/2.

 

The slope of a line on a graph (m) is the change in y divided by the change in x and is shown as follows:

 

y = mx + b where 

m is the slope

b is the y-intercept

 

This is called the slope-intercept form for the line equation.

 

Start by putting the problem line in the slope-intercept format:

 

4x = y- 8

Add 8 to both sides of the equation gives:

y = 4x +8

 

From the slope-intercept line description above, the slope (m) is the coefficient of x which is 4.

 

Because the line perpendicular to this line will have a slope which is the negative reciprocal, then its slope is -1/4.

 

Therefore, the perpendicular line can be expressed in the slope-intercept way as follows:

 

y = (-1/4)x + b

 

We can find "b", the y-intercept because we know from the problem that the line goes through point (2,-7).

 

That means that an x-value of 2 and a y-value of -7 satisfies the equation.

Plugging these values into the equation above gives:

 

y = (-1/4)x + b

-7 = (-1/4)(2) + b

-7 = -1/2 + b

Adding 1/2 to both sides of the equation to get b gives

b = -7 + 1/2 = -6½

 

So the formula for the perpendicular line would be y = (-1/4)x - 6½