Question

Select all statements that are true about the linear equation.

Answer 1

Answer:

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

Step-by-step explanation:

we have the linear equation

$y=\frac{1}{3}x+2$

This is the equation of the line in point slope form

where

the slope is $m=\frac{1}{3}$

the y-intercept is $b=2$

Remember that

If a ordered pair is on the graph of the linear equation, then the ordered pair must satisfy the linear equation

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

Verify each statement

case 1) The graph of the equation is a single point representing one solution to the equation

The statement is false

Because the graph of the equation is the set of all points that are solutions to the equation

case 2) The point (9,5) is on the graph of the equation

The statement is true

Because

For x=9, y=5

substitute 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 true

so

the ordered pair satisfy the linear equation

therefore

The point is on the graph of the equation

case 3) The graph of the equation is the set of all points that are solutions to the equation

The statement is true

case 4) The point (-3,-1) is on the graph of the equation

The statement is false

Because

For x=-3, y=-1

substitute 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 true

so

the ordered pair not satisfy the linear equation

therefore

The point is not on the graph of the equation