The line on the graph passes through to points A (1, 3) B (7, 1)

a. Gradient of line AB is

b. The gradient of a line perpendicular to line AB is 3

c. The equation of a line passing through point (4,2) and perpendicular to AB is

Step-by-step explanation:

a.

Given

Point A (1, 3) B (7, 1)

Required

Gradient of AB

Gradient of a line is represented by m

m is calculated using the following formula

Where the general representation of the coordinates are

From the given data, we have that

So, from there we know that

becomes

b.

Required

Find the gradient of a line perpendicular to AB

Recall that gradient of a line is represented by m

The condition for perpendicularity is that

In (a) above, we solved the gradient of line AB to be

Let represent gradient of line AB

Hence,

Substitute for in  

This will give

Multiply both sides by -3

Hence, the gradient of a line perpendicular to line AB is 3

c.

Required

Find the equation of a line passing through point (4,2) and perpendicular to AB

Equation is calculated using the gradient formula

Since only one point is known, the formula is represented as follows

Where

Since, the line is perpendicular to line AB, then its gradient m is equal to 3 (as calculated in b above)

So, we have

By substitution

becomes

Multiply both sides by x - 4

Open brackets

Make y the subject of formula

Reorder

Hence, the equation of a line passing through point (4,2) and perpendicular to AB is

c - they will have the same distribution

step-by-step explanation:

this is the only one that could make sense. : )