Linear equations
Concept
Linear equations, or a straight line on a graph, generally consist of two variables, x, and y - as well as slope.
Utilization
You have been provided a linear equation in slope-intercept form (y=mx+b). Let's look at the true and false statements now:
The graph of the equation is the set of all points that are solutions to the equation, TRUE or FALSE. The answer to this is true, because any point on the line should provide a valid solution to the problem. TRUE
The point (10, 3) is on the graph of the equation. We have already determined that in order for a point to be on the line - it must be a solution... so, plug it in and test:
[tex]y = 12x - 2\\3 = 12(10) - 2\\3 = 120 - 2\\3 = 118[/tex]
3 is not equal to 118, so the point (10,3) is not on this line. FALSE
The point (−2,−1) is on the graph of the equation. Use the same setup as before:
[tex]y = 12x - 2\\-1 = 12(-2) - 1\\-1 = -24 - 1\\-1 = -25[/tex]
-1 is not equal to -25, so this point is once again, not on the line. FALSE
The graph of the equation is a single point representing one solution to the equation. This is nearly the inverse of the first statement, so we can rule this out as well. FALSE
Answer
The only true statement here seems to be The graph of the equation is the set of all points that are solutions to the equation. Hope this helps you!
