Question

The diagram shows a set of coordinate axes superimposed on the cross section of a sloping roof of height, h metres and width w metres. The equation of one half of the cross section is y= -0.7x+1.9.

Answer 1

a) What is the equation of the other half of the cross section? b) What is the width of the roof, w, to the nearest tenth of a metre? c) State the domain and range of each function that states each half of the roof.

Answer 2

Why is the answer for a) y = 0.7x + 1.9 and b) 5.4 m?

Answer 3

for (a), the line on the left has the same y-value as the line on the right if you replace x by its negative.

Answer 4

for (b), when the line crosses the x-axes, the value of y is zero. so we get:
0 = -0.7x + 1.9
if you solve this for x, you will get half the width.

Answer 5

ohh, okay, so why shouldn't it not -0.7x + 1.9

Answer 6

wait, what is the x- axis? like the horizontal axis?
So I basically double it?

Answer 7

yes - the x-axis is the horizontal axis

Answer 8

and yes, you double the resulting value to get w

Answer 9

ohh, okay. So when the line basically passes the horizontal axis then y-value becomes o ex. say (6,0)?
Ohh..

Answer 10

for a) you are given: y = -0.7x + 1.9
so, to get the equation for the line on the left, you replace x with -x to get:
y = -0.7(-x) + 1.9 = 0.7x + 1.9

Answer 11

why do I replace x with -x? Oh because the x-values on the left-side are negative?

Answer 12

yes - I think you are beginning to understand these types of equations now :)

Answer 13

ohh, thank you!

Answer 14

yw