Question

Select all statements that are true about the linear equation.

Answer 1

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:

$y = 12x - 2\\3 = 12(10) - 2\\3 = 120 - 2\\3 = 118$

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:

$y = 12x - 2\\-1 = 12(-2) - 1\\-1 = -24 - 1\\-1 = -25$

-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!