How Do You Find the Slope-Intercept Form with Given Intercepts?

[rcmango]

Homework Statement

find the slope-intercept form for the line satisfying the following conditions
x intercept 2, y intercept 2/3

Please let me know if I solved this correctly. Thankyou.

Homework Equations

The Attempt at a Solution

2, 0

0,2/3

(2/3 -0) / (0 - 2)

2/3 / -2/1

2/3 * -1/2

-2/6 == -1/3

slope intercept form
so y = -1/3x + 2/3

 

[LCKurtz]

That is correct.

 

[rcmango]

thanks.

 

[Mentallic]

2/3 * -1/2

-2/6 == -1/3

Rather than instantly multiplying numerators and denominators together, then cancelling, you should cancel first! The common factor of 2 in the numerator and denominator of 2/3 * -1/2 should be canceled to leave you with 1/3 * -1/1 = -1/3

 

[rcmango]

Okay, thanks for the advice, ill definitely keep that in mind. So denominators, and numerators from opposite equations can cancel early for fractions.

 

[Mentallic]

Yep!

It's because we can do things like

$$\frac{a}{c}\cdot\frac{b}{d}=\frac{ab}{cd}=\frac{ba}{cd}=\frac{b}{c}\cdot\frac{a}{d}$$

Which is why it works.