Question

The line given by the equation y= -3x+1
goes through the points (1,a) and (b,4).
2a-3b= ?

a. -2
b. -1
c. 0
d. 1
e. Cannot be determined from given
information

Answer 1

if you know \(x\) then you know \(y\) and vice versa

Answer 2

if \(x=1\) then \(y=-3\times 1+1=-2\) so \((1,-2)\) is on the graph, i.e. \(a=-2\)

Answer 3

It is simple if you graph the equation.

Look where x = 1, y = -2.
And where y = 4, x = -1

So then you substitute a and b in to the second equation.

a = -2
b = -1

2a - 3b =
2(-2) - 3(-1) =
-4 - (-3) =
-4 + 3 = -1

So -1 is the answer.