To determine if a point in the form of an ordered pair is a solution to the equation, we substitute the ordered pair in for x and y in the equation and simplify to see if the equation is a true statement. Testing (6, 0)=(x,y) ; let x=6 and y=0, and see if this makes the equation true. => => => => This shows that (6, 0) is a solution to the equation . Now test (-3, -2)=(x, y) let x=-3 and y=-2, and see if this makes the equation true. => => => This shows that (-3, -2) is NOT a solution to the equation. To review this in more detail, follow this link to our OpenStax Textbook (Intermediate Algebra), and scroll down the section of the text that has a box with the title "Solution of a Linear Equation in Two Variables".

One way to find the slope and the y-intercept of a line defined by its equation is to rewrite the equation in slope-intercept form. Recall that a linear equation is in slope intercept for when the equation is written in the form where is the slope and is the y-intercept. Given the equation , we work to solve for y. First, we subtract 3x from both sides to get Still looking to get y by itself, we divide both sides by -1 Simplify the right hand side The equation is now in slope intercept form m=3 and b=-12. This means the slope is 3 and the y-intercept is (0, -12). Want to review this idea further?  Follow this link to our OpenStax Textbook:  Intermediate Algebra, and scroll to the section titled "Graph a Line Using its Slope and Intercept."  Example 3.16 describes how to identify the slope and the y-intercept given the equation of a line.

Let's start by finding the x-intercept. An x-intercept is where the graph crosses the x-axis. A point on the x-axis comes in the form (x, 0). Because of this, when finding the x-intercept, we let y=0 in the equation, and solve for x. That is: => => This means the x-intercept is the point (6, 0). Now, let's look at one way of finding the y-intercept. A y-intercept is where the graph crosses the y-axis. A point on the y-axis comes in the form (0, y). Because of this, when finding the y-intercept, we let y=0, and solve for y. That is: => => This means the y-intercept is the point (0, -4). If you would like to review this topic further, follow this link to the OpenStax Textbook:  Intermediate Algebra.  Then, scroll down the section titled "Find x- and y-intercepts."