We are finding linear equations using all sorts of information.  We can find an equation if we are given 2 points.

We can graph the points and sketch our line.  Our graph can help us find the slope by using a triangle and comparing the rise and run.  We can also use a table and look at the difference in y values and x values and show the slope as the change in y value divided by the change in x value. The next calculation is to figure out the “b” value or the constant.

Here’s a different question, where a table was used to find the constant (the value of y when x=0).  The slope was found (-4/7 or -0.57) and then the table was filled in where for each increase in 1 for x, the y value decreased by 0.57. Another way to solve for the b value is to substitute the value of one given point for x and y in the equation y=mx+b.

Y=-0.57x+b

Sub in the given point (4,-9)

-9=-0.57(4)+b

-9=-2.28+b

-9+2.28=-2.28+2.28+b

-6.72=b

(Note, the difference in value from above is due to rounding)

We looked at some complex problems where we are looking for a line that is parallel to a given line, and has the same y intercept as another given line.  We needed to isolate y in the equations and then extract the useful information (either m or b) and use that to create our new line. We’re working hard and helping each other 