Determine the slope of the points (-2, -7) and (0, -1)

First let's find the slope of the line through the points  and  

Note:  is the first point . So this means that x%5B1%5D=-2 and y%5B1%5D=0.

Also,  is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=3.

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.

m=%283-0%29%2F%280--2%29 Plug in y%5B2%5D=3, y%5B1%5D=0, x%5B2%5D=0, and x%5B1%5D=-2

m=%283%29%2F%280--2%29 Subtract 0 from 3 to get 3

m=%283%29%2F%282%29 Subtract -2 from 0 to get 2

So the slope of the line that goes through the points  and  is m=3%2F2

Now let's use the point slope formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula

y-0=%283%2F2%29%28x--2%29 Plug in m=3%2F2, x%5B1%5D=-2, and y%5B1%5D=0

y-0=%283%2F2%29%28x%2B2%29 Rewrite x--2 as x%2B2

y-0=%283%2F2%29x%2B%283%2F2%29%282%29 Distribute

y-0=%283%2F2%29x%2B3 Multiply

y=%283%2F2%29x%2B3 Simplify

So the equation that goes through the points  and  is y=%283%2F2%29x%2B3

Notice how the graph of y=%283%2F2%29x%2B3 goes through the points  and . So this visually verifies our answer.

Graph of y=%283%2F2%29x%2B3 through the points  and

Step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: