Solve for y; calculate a few sample points (plug in a value for x, then calculate the corresponding value for y); plot on the graph. Two points should be enough in theory (this equation is a straight line), but a third point helps you confirm that your calculations are correct.Solve for y; calculate a few sample points (plug in a value for x, then calculate the corresponding value for y); plot on the graph. Two points should be enough in theory (this equation is a straight line), but a third point helps you confirm that your calculations are correct.Solve for y; calculate a few sample points (plug in a value for x, then calculate the corresponding value for y); plot on the graph. Two points should be enough in theory (this equation is a straight line), but a third point helps you confirm that your calculations are correct.Solve for y; calculate a few sample points (plug in a value for x, then calculate the corresponding value for y); plot on the graph. Two points should be enough in theory (this equation is a straight line), but a third point helps you confirm that your calculations are correct.
In the same coordinate space, i.e. on the same set of axes: -- Graph the first equation. -- Graph the second equation. -- Graph the third equation. . . -- Rinse and repeat for each equation in the system. -- Visually examine the graphs to find the points (2-dimension graph) or lines (3-dimension graph) where all of the individual graphs intersect. Since those points or lines lie on the graph of each individual graph, they are the solution to the entire system of equations.
You write it as: y = 5x-4 Then you calculate a few sample points, plot them, and draw a straight line through them. Since the equation is linear, two points are enough, in theory, but it is usually recommended to plot a third point, as a verification.
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In theory you only need 2 since 2 points in the plane determine a line. However, we all make mistakes ( I make plenty!) and making sure that third point falls on the line you found from the other two is a good way to check for errors.
Solve for y; calculate a few sample points (plug in a value for x, then calculate the corresponding value for y); plot on the graph. Two points should be enough in theory (this equation is a straight line), but a third point helps you confirm that your calculations are correct.Solve for y; calculate a few sample points (plug in a value for x, then calculate the corresponding value for y); plot on the graph. Two points should be enough in theory (this equation is a straight line), but a third point helps you confirm that your calculations are correct.Solve for y; calculate a few sample points (plug in a value for x, then calculate the corresponding value for y); plot on the graph. Two points should be enough in theory (this equation is a straight line), but a third point helps you confirm that your calculations are correct.Solve for y; calculate a few sample points (plug in a value for x, then calculate the corresponding value for y); plot on the graph. Two points should be enough in theory (this equation is a straight line), but a third point helps you confirm that your calculations are correct.
In the same coordinate space, i.e. on the same set of axes: -- Graph the first equation. -- Graph the second equation. -- Graph the third equation. . . -- Rinse and repeat for each equation in the system. -- Visually examine the graphs to find the points (2-dimension graph) or lines (3-dimension graph) where all of the individual graphs intersect. Since those points or lines lie on the graph of each individual graph, they are the solution to the entire system of equations.
You write it as: y = 5x-4 Then you calculate a few sample points, plot them, and draw a straight line through them. Since the equation is linear, two points are enough, in theory, but it is usually recommended to plot a third point, as a verification.
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Step 1: Solve for y so that your equation is in the form of y=mx+b Step 2: your m value is your y- intercept. So put the point (0,m) on the graph Step 3: your b value is your slope of the equation. If your b value is already a fraction then the numerator is your "rise" and the denominator is your "run." If your b value is not a fraction then just make it into one by putting a fraction bar and a 1 underneath it. Now starting from the first point you put, go up or down the amount of your "rise" and mark the point. Positive is up and negative is down. For example if your "rise" is -3 then go down three points from your y intercept. Now from your second point, go left or right depending on your "run" and make a point. Positive is right and negative is left. For example, if my "run" is 5 then I will move 5 right and make a point. Step 4: Connect your first and third point with a straight line and extend the line. Put arrow heads on both ends of your line and that is your equation of a line on a graph.
Four points can produce a polynomial of at most the third order - a cubic. It is, of course, possible that the 4 points are collinear.
In theory you only need 2 since 2 points in the plane determine a line. However, we all make mistakes ( I make plenty!) and making sure that third point falls on the line you found from the other two is a good way to check for errors.
Write this equation in slope-intercept form:4x + 3y = 12 subtract 4x to both sides3y = -4x + 12 divide by 3 to both sidesy = -(4/3)x + 4 since the y intercept is 4, then one point is (0, 4)Let x = 3, then y = 0. So the second point is (3, 0)Let x = -3, then y = 8. So the third point is (-3, 8)Now that you have three points, plot them in a coordinate system and connect those points. The line that passes through these points is the graph of the function y = -(4/3)x + 4.
You need to know the domain over which you are required to graph the function. Suppose it is between 0 and 10. Choose x = 0 and substitute this value into the equation y = 6x + 5. It becomes y = 6*0 + 5 = 0 + 5 = 5. So mark the point (0, 5) on the grid. Choose x = 10 and substitute this value into the equation y = 6x + 5. It becomesy = 6*10 + 5 = 60 + 5 = 65. So mark the point (10, 65) on the grid. You can join these two points with a straight line and you are done. However, it is safer to do a third point, say x = 5.The equation then gives y = 6*5 + 5 = 30 + 5 and so mark the point (5, 35). If the 3 points are in the same straight line (they are collinear) you are home. If not, you have made a mistake in one of your calculations.
The one to the lower left of the origin.
For each linear equation the procedure is the same: Suppose the equation is y = mx + c where x and y are the two variables and m and c are two constants. Set x = 0 so that the equation becomes y = c. Mark the point P = (0, c) on the coordinate plane. Set y = 0 so the equation becomes 0 = mx + c so that x = -c/m. Mark the point Q = (-m/c, 0) on the plane. Join PQ with a straight line and extend in both directions. You may wish to select another value of x (or y), substitute into the equation and solve. This will give the coordinates of a third point, R. The only reason for doing this is that if R is not on the line PQ then you know you have made a mistake. Repeat for other equations.