Question

А
B
The scale factor that takes A onto B is
The scale factor that takes B onto A is

Answer 1

Let,

x₁, y₁ = 2, 2

x₂, y₂ = 6, 10

a.) The slope of the line.

`\text{ Slope = }(y_2-y_1)/(x_2-x_1)`
`\text{ = }\frac{\text{ 10 - 2}}{\text{ 6 - 2}}\text{ = }\frac{\text{ 8}}{\text{ 4}}`
`\text{ Slope = 2}`

Therefore, the slope of the line is 2.

b.) The y-intercept of the line.

Substitute slope = m = 2 and x, y = 2, 2 in y = mx + b

`\text{ y = mx + b}`
`\text{ 2 = 2(2) + b}`
`\text{ 2 = 4 + b }\rightarrow\text{ b = 2 - 4}`
`\text{ b = y-intercept = -2}`

Therefore, the y-intercept is -2.

For us to answer the other 2 questions, let's first complete the equation of the graph.

Substitute slope = 2 and y-intercept = -2 in the y = mx + b

y = mx + b

y = (2)x + (-2)

y = 2x - 2

The equation of the line is y = 2x - 2

c.) Finding the value of a.

x = a

y = 8

We get,

`\text{ y = 2x - 2}`
`\text{8 = 2a - 2}`
`\text{ 2a = 8 + 2 = 10}`
`\text{ }\frac{\text{2a}}{\text{ 2}}\text{ = }\frac{\text{10}}{\text{ 2}}`
`\text{ a = 5}`

Therefore a = 5

d.) Finding the value of b.

x = 4

y = b

`\text{ y = 2x - 2}`
`\text{ b = 2(4) - 2}`
`\text{ b = 8 - 2 = 6}`

Therefore, b = 6