Question

Select all statements that are true about the linear equation.

y=1/2x−4


a.The point (−6,7) is on the graph of the equation.

b.The point (−4,−6) is on the graph of the equation.

c.The graph of the equation is a single point representing one solution to the equation.

d.The graph of the equation is the set of all points that are solutions to the equation.

Answer 1

Check all options:

A. The point (−6,7) is on the graph of the equation
`y=(1)/(2)x-4.` Substitute x=-6, y=7 and get

`7=(1)/(2)\cdot (-6)-4,\\ \\7=-3-4,\\ \\7=-7.`

This is false equality, thus option A is false.

B. The point (−4,-6) is on the graph of the equation
`y=(1)/(2)x-4.` Substitute x=-4, y=-6 and get

`-6=(1)/(2)\cdot (-4)-4,\\ \\-6=-2-4,\\ \\-6=-6.`

This is true equality, thus option B is true.

C and D. Look at the attached diagram for the graph of the function
`y=(1)/(2)x-4.` You can see that the graph is the solid line, therefore, the graph of the equation is the set of all points that are solutions to the equation not the graph of the equation is a single point representing one solution to the equation. Option C is false, option D is true.

Answer: correct options are B and D.