Question

select all statements that are true about the linear equation.
$y = 4x - 3$
the graph of the equation is a single point representing one solution to the equation.
the point $(0, - 3)$ is on the graph of the equation.
the point $(1, 1)$ is on the graph of the equation.
the graph of the equation is the set of all points that are solutions to the equation.

Explanation:

Step1: Recall linear - equation graph property

A linear equation $y = mx + b$ ($m
eq0$) has infinitely many solutions and its graph is a line, not a single point. So the first statement is false.

Step2: Check if $(0,-3)$ is on the graph

Substitute $x = 0$ into $y=4x - 3$. We get $y=4\times0 - 3=-3$. So the point $(0, - 3)$ is on the graph of the equation.

Step3: Check if $(1,1)$ is on the graph

Substitute $x = 1$ into $y = 4x-3$. We have $y=4\times1-3=1$. So the point $(1,1)$ is on the graph of the equation.

Step4: Recall the definition of the graph of an equation

The graph of an equation is the set of all points $(x,y)$ that satisfy the equation. So the fourth statement is true.

Answer:

The point $(0, - 3)$ is on the graph of the equation.
The point $(1,1)$ is on the graph of the equation.
The graph of the equation is the set of all points that are solutions to the equation.