Two simple questions. Gradient of straight line(Coordinate geometry)

Question

- 14. (a,b) lies on a straight line of gradient 32 . If a is increased by 6, what does b increase by?

 

- 15. (a,b) lies on a straight line of gradient –2. If a is increased by 2, what does b change by?

 

 

 

 Whats the formula to work out these questions?

Answer 1

Q14

Given, slope/gradient of line, m = 32

The 2 points here are (a,b) and (a+6,y2)

 

For 2 points (x1, y1) and (x2, y2) on a line,

  m = (y2-y1)/(x2-x1)

 

Using this formula,

32 = (y2-b)/(a+6-a)

    = (y2-b)/6

y2-b = 32*6 = 192

y2 = b+192

So, b increases by 192 when a increases by 6

 

Q15

Given, slope/gradient of line, m = -2

The 2 points here are (a,b) and (a+2,y2)

For 2 points (x1, y1) and (x2, y2) on a line,
m = (y2-y1)/(x2-x1)

Using this formula,

-2 =(y2-b)/(a+2-a)

    = (y2-b)/2

y2-b = -2(2) = -4

y2 = b-4

 

So, b decreases by 4 when a increases by 2