Part a. write an equation of a line that is perpendicular to the line y = 2/3x + 5 and passes through the point (4, 0).
part b: explain how you determine the equation in 3-4 sentences usin at least 6 of the words below.
slope
y-intercept
x-intercept
perpendicular
opposite
reciprocal
substituted/substitution
slope-intercept form
ordered pair

The equation of line is , which is perpendicular to the line

(A). Equation of given line is,  

Comparing above equation of line from slope - intercept equation of line

So, slope of given line is,  

Since, The perpendicular line slope will be the opposite reciprocal of the original slope.

So, slope of perpendicular line is, =

          Slope =

Equation of line perpendicular to given line,

Since, line passing through (4, 0)

Thus,  

Therefore, equation of line perpendicular to given line is,  

(B).The perpendicular line slope will be the opposite reciprocal of the original slope.

   Equation of perpendicular line in slope intercept form,,

     Y - intercept is 6.

   Slope of perpendicular line is

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Step-by-step explanation:

Given:

The given equation of the line that passes through the point (4, 0).

Part A.

The equation of the line.

-----------(1)

Where:

m = Slope of the line

c = y-intercept

The given equation of the line.

Comparing the given equation with equation 1.

The slope of the line is and y-intercept

We know that the slope of the perpendicular line is .

So the slope of the perpendicular line is .

Using point slope formula we write the equation of the perpendicular line that passes through the point (4, 0).

Now we substitute the slope of the perpendicular line and from point (4, 0) in above equation.  

Therefore the perpendicular line equation is .

Part B.

1. The slope of the perpendicular line is .

2. The y-intercept of the perpendicular line is 6.

3. The equation of the line is perpendicular to the equation of line .

h

step-by-step explanation: