mathBeats: Equation of a Line (The Businessperson Is a Climber)

A world of one point and a slope

A businessperson facing the climb

The businessperson waits for (y is m x plus b)

But the intercept b is missing, the path's hard to find

No intercept? Don't panic now

You're a climber! (You're a climber!)

Look where you stand: (x one, y one)

That's your base camp, where the journey's begun

With a starting point and a direction, a path appears

(x, y) is the place you're meant to reach

(y minus y one) is the height you gain (Rise!)

(x minus x one) is the horizontal run (Run!)

Their ratio always stays the same

That's business performance, slope m, by name

The climber's magic formula, make it your own

(y minus y one equals, m times x minus x one!)

When you know the start, (x one, y one)

And you know how fast you grow, slope m

The future (x, y) is already shown

The line's equation lights the road you're on

(y minus y one) is the height you gain (Rise!)

(x minus x one) is the horizontal run (Run!)

Their ratio always stays the same

That's business performance, slope m, by name

The climber's magic formula, make it your own

(y minus y one equals, m times x minus x one!)

This formula is the climber's map

Open the brackets, watch it change

It turns into (y is m x plus b)

Follow it down (x is zero, see?)

Now the intercept comes into view

That's b, that's b, waiting for you

Hey, climber! Ready to start the ascent? (Quiz time!)

Question one

The base camp is at (2, 5). The slope is one half

When x reaches 6, how high is y?

Question two

The map reads (y minus one is four times (x plus three))

What's the slope-intercept form, and what is b?