Question

True or false: this is a linear function (if graphed would it make a straight line?)

Answer 1

Step 1

Pick two consecutive points and find the equation of a straight line.

(7,-1) and (5,0)

Equation of a straight line

y = mx + c

for (7,-1)

-1 = 7m + c ....................... equation 1

for (5,0)

0 = 5m + c ...................... equation 2

make c subject of relation from equation 2

c = -5m

Substitute c in equation 1

-1 = 7m - 5m

-1 = 2m

m = -1/2

c = -5(-1/2)

c = 5/2

`y\text{ = }(-1)/(2)x\text{ + }(5)/(2)`

From the equation above, the table shows a linear function.

Every x input in the equation, give the correct y output.