Question

Blaine was asked to write a linear equation in slope-intercept form and was given that (3,2) and (1,-6) were on the line. Blaine thought he did the problem correctly, however his teacher said he made a mistake. His work is below...

y = mx + b
Step 1: Find Slope

m = y2 - y1x2 - x1 = 3 - 12 - (-6) = 28 =14

Step 2: Find y-intercept
m = 14(1,-6)
y = mx + b
-6 = 14(1) + b
-6 = 14+ b
-6.25 = b

Step 3: Write equation using slope and y-intercept
m = 14and b =-6.25
y = mx + b
y = 14x - 6.25 (Final Equation)

In 2-3 paragraphs…
1) Find and explain Blaine’s mistake
2) What would his new slope and y-intercept be and explain how to calculate each one
3)Tell me the correct equation in slope-intercept form that Blaine should’ve came up with.
*****BE DETAILED in your writing and explanations.

Answer 1

1)The equation of the line in slope intercept form is


`y=mx+b`

where
`m=(y_2-y_1)/(x_2-x_1)`

Blaine got this right.

Let
`(x_1,y_1)=(3,2)` and
`(x_2,y_2)=(1,-6)`.

We find the slope by substituting the values into the slope formula;


`m=(-6-2)/(1-3)`


`m=(-8)/(-2)`


`m=4`

Blaine made a mistake here. He substituted the x-values for the y-values and vice-versa.

2) His new slope is 4.

To find the y-intercept, we substitute the slope and the point (1,-6) into the formula

This gives;


`-6=4(1)+b`


`-6-4=b`


`b=-10`

3) We now substitute the slope m=4 and y-intercept b=-10

The correct equation Blaine should have come up with is


`y=4x-10`