Standard Form

Question

Cody was given two points (1/2.5) and (2/3.2), on a line and asked to create a linear equation in standard form. Cody's work is shown, identify and errors and correct them

 

y=2=- 1/2(x-2/3)

 

y-2 = 1/2x + 1/3

 

2y - 4 = -x + 2/3

 

x +2y = 14/3

 

 

Cody made an error while finding the slope: -3/1/6 =-3(     )= (     ) Cody also should have multiplied both sides of the equation by (          ), not 2, and should have multiplied all the terms.  The Equation should be (                )

Answer 1

Cody used the point-slope form to find the equation of the line, which is 

 

y - y₀ = m(x - x₀)   where m = slope and (x₀, y₀) is a point on the line

 

The slope m can be found by calculating rise over run, that is, the difference of the two y-coordinates given and the difference of the two x-coordinates.

 

It appears that the two points on the line are (2/3, 2) and (1/2, 5). In that case, the slope is:

 

(5 - 2)/(1/2 - 2/3) = 3/(3/6 - 4/6) = 3/(-1/6) = 3 * (-6) = -18   Why?

 

When you divide by a fraction, you have to find the reciprocal of the fraction and then multiply. Hence, the slope of the line is -18.

 

The equation of the line is now y - 2 = -18(x - 2/3)    using the point (2/3, 2)

 

In standard form, the equation of a line is Ax + By = C, where A, B, and C are constants.

 

Let's put our equation of the line into this form.

 

y - 2 = -18x + 12

18x + y - 2 = 12

18x + y = 14