Two points A (-2, 9) and B (4, 8) lie on a line l. (i) Find the slope of the line l. (2)marks (ii) Find the coordinates of the midpoint of the points A and B (iii) Find the distance between points A and B. (i). A line “t” is parallel to 3y = 6x + 9. Find the slope of this line “t”. (ii) Another line “r” is perpendicular to the line 3y = 6x + 9. Find the gradient of the line “r”.

Question 1:

The coordinates are A(-2,9) and B(4,8)

(i) Slope =

Slope =

Slope =

Slope =

(ii) M(x,y) =

=> M(x,y) =

=> M(x,y) =

=> M(x+y) = (1 , 8.5)

(iii) Distance Formula =

D =

D =

D =

D = units

Question 2:

(i) The given equation is:

=> 3y = 6x+9

=> 3y = 3(2x+3)

Dividing both sides by 3

=> y = 2x+3

Where Slope = m = 2 and y-intercept = b = 3

Parallel lines have equal slopes

=> So,  Slope of line "t" = 2

(ii) Line 3y = 6x+9 has a slope of 2

=> Perpendicular lines have a slope of negative reciprocal such that multiplying their slopes will give -1

=> Gradient of line "r" = -1/2

the answer is 175.4379

step-by-step explanation:

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.