Q:

# Select all statements that are true about the linear equation.y= 1/3x + 2The graph of the equation is a single point representing one solution to the equation.The point (9,5) is on the graph of the equation.The graph of the equation is the set of all points that are solutions to the equation.The point (-3,-1) is on the graph of the equation.​

Accepted Solution

A:
Answer:The point (9,5) is on the graph of the equationThe graph of the equation is the set of all points that are solutions to the equationStep-by-step explanation:we have the linear equation$$y=\frac{1}{3}x+2$$This is the equation of the line in point slope formwherethe slope is $$m=\frac{1}{3}$$the y-intercept is $$b=2$$Remember thatIf a ordered pair is on the graph of the linear equation, then the ordered pair must satisfy the linear equationThe graph of the equation is the set of all points that are solutions to the equationVerify each statementcase 1) The graph of the equation is a single point representing one solution to the equationThe statement is falseBecause the graph of the equation is the set of all points that are solutions to the equationcase 2) The point (9,5) is on the graph of the equationThe statement is trueBecauseFor x=9, y=5substitute the value of x and the value of y in the linear equation$$5=\frac{1}{3}(9)+2$$$$5=3+2$$$$5=5$$ ----> is truesothe ordered pair satisfy the linear equationthereforeThe point is on the graph of the equationcase 3) The graph of the equation is the set of all points that are solutions to the equationThe statement is truecase 4) The point (-3,-1) is on the graph of the equationThe statement is falseBecauseFor x=-3, y=-1substitute the value of x and the value of y in the linear equation$$-1=\frac{1}{3}(-3)+2$$$$-1=-1+2$$$$-1=1$$ ----> is not truesothe ordered pair not satisfy the linear equationthereforeThe point is not on the graph of the equation