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.[br][br]Testing (6, 0)=(x,y)[br][br][math]y=\frac{2}{3}x-4[/math]; let x=6 and y=0, and see if this makes the equation true.[br][br][math]0=\frac{2}{3}\left(6\right)-4[/math] => [math]0=\frac{2}{3}\left(\frac{6}{1}\right)-4[/math] => [math]0=\frac{2}{1}\left(\frac{2}{1}\right)-4[/math] =>[math]0=4-4[/math] => [math]4=4[/math][br][br]This shows that (6, 0) is a solution to the equation [math]y=\frac{2}{3}x-4[/math].[br][br]Now test (-3, -2)=(x, y)[br][br][math]y=\frac{2}{3}x-4[/math] let x=-3 and y=-2, and see if this makes the equation true.[br][br][math]-2=\frac{2}{3}\left(-3\right)-4[/math] => [math]-2=\frac{2}{3}\left(-\frac{3}{1}\right)-4[/math] => [math]-2=-2-4[/math] =>[math]-2\ne-6[/math][br][br]This shows that (-3, -2) is NOT a solution to the equation[math]y=\frac{2}{3}x-4[/math].[br][br][url=https://openstax.org/books/intermediate-algebra-2e/pages/3-1-graph-linear-equations-in-two-variables#fs-id1167835400321]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".[/url][br]

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.[br][br]Recall that a linear equation is in slope intercept for when the equation is written in the form [math]y=mx+b[/math] where [math]m[/math] is the slope and [math]\left(0,b\right)[/math] is the y-intercept. [br][br]Given the equation [math]3x-y=12[/math], we work to solve for y. First, we subtract 3x from both sides to get[br][br][math]-y=-3x+12[/math][br][br]Still looking to get y by itself, we divide both sides by -1[br][br][math]y=\frac{-3x+12}{-1}[/math][br][br]Simplify the right hand side[br][br][math]y=3x-12[/math][br][br]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).[br][br][br][url=https://openstax.org/books/intermediate-algebra-2e/pages/3-2-slope-of-a-line#fs-id1167835342973]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.[/url][br][br]

Let's start by finding the x-intercept. [br][br]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:[br][br][math]2x-3\left(0\right)=12[/math] => [math]2x=12[/math] => [math]x=6[/math][br][br]This means the x-intercept is the point (6, 0).[br][br]Now, let's look at one way of finding the y-intercept.[br][br]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:[br][br][math]2\left(0\right)-3y=12[/math] => [math]-3y=12[/math] => [math]y=-4[/math][br][br]This means the y-intercept is the point (0, -4).[br][br][url=https://openstax.org/books/intermediate-algebra-2e/pages/3-1-graph-linear-equations-in-two-variables#fs-id1167827987818]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."[/url][br]