Question

For the line y = 7x+6 show that the slope is 7 regardless of the points (x1, y1) and (x2, y2) you use to calculate the slope. (Hint: Substitute x1 and x2 into the equation to obtain expressions for y1 and y2.)

Answer 1

You should choose some arbitrary values for x1 and x2 and find their corresponding y values, substitute into the equation, and show that the output is always the same.

\[x_1=5, x_2=2\]\[y_1=7(5)+6, y_2=7(2)+6\]\[y_1=41, y_2=20\]\[slope=rise/run\]\[slope=y_2-y_1/x_2-x_1\]\[slope=41-20/5-2\]\[slope=21/3\]\[slope=7\]

Dot his again with two other arbitrary values of x2 and x1, and compare the results.