To determine if a point is on the line given the equation of the line, plug in the coordinate points into the equation. Remember that coordinate points are written as (x, y), so plug the x-value in for the x variable and the y-value in for the y variable, then simplify. If the equation is true, meaning the two sides equal each other, then the point is on the line of the equation. If the equation is not true, meaning the two sides do not equal each other, then the point is not on the line of the equation.
This problem it's going to be a little different from some of the formats you've seen before. Notice it's not a multiple choice problem, I don't get to choose which answer is right. It doesn't say, 'Which one of the following is right?' This is like two different problems combined into one.
Without graphing determine whether each point is on the line y equals 3x plus 2 my answers are going to look like either yes or no for each one of these two different points. Here's how it's going to go.
Each point has an x number that comes first and then the y number. I'm going to substitute in to the equation and see if I get a true equality or not. For example if my x number is one and my y number is six, let's see if this is true. Is 6 equal to 3 times my x number plus 2, is 6 equal to 5? No so this point is not on the line I didn't have to graph it and I can already tell you that guy wouldn't be on the line.
Let's try this one, my x number is -2, my y number is -4. So is it true that -4 is equal to three times my x number plus two? When you simplify you can see yes, -4 is equal to-4, hurray! That means without graphing I could tell you this point would be on the line. This is a really useful technique for anyone who doesn't like graphing or if you tend to make mistakes when you graph this will be really useful for you. You'll be able to tell whether or not a point is on the line without having to draw the graph. By substituting in the x,y coordinate pairs and see if you get an equality or not.
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