3x 2y 16 in slope intercept form

Step 3: Plot the y -intercept point on the graph. Step 4: Use the slope to find a second point on the graph.

In previous chapters we solved equations with one unknown or variable. We will now study methods of solving systems of equations consisting of two equations and two variables. Upon completing this section you should be able to: Represent the Cartesian coordinate system and identify the origin and axes. Given an ordered pair, locate that point on the Cartesian coordinate system. Given a point on the Cartesian coordinate system, state the ordered pair associated with it.

3x 2y 16 in slope intercept form

The slope of a line is its vertical change divided by its horizontal change, also known as rise over run. When you have 2 points on a line on a graph the slope is the change in y divided by the change in x. Input two points using numbers, fractions, mixed numbers or decimals. The slope calculator shows the work and gives these slope solutions:. You will also be provided with a custom link to the Midpoint Calculator that will solve and show the work to find the midpoint and distance for your given two points. Here you need to know the coordinates of 2 points on a line, x 1 , y 1 and x 2 , y 2. Say you know two points on a line and their coordinates are 2, 5 and 9, Find slope by finding the difference in the y points, and divide that by the difference in the x points. Using the coordinates of one of the points on the line, insert the values in the x1 and y1 spots to get an equation of a line in point slope form. Lets use a point from the original example above 2, 5 , and the slope which we calculated as 2. Put those values in the point slope format to get an equation of that line in point slope form:. If you simplify the point slope equation above you get the equation of the line in slope intercept form. Continue to work the equation so that y is on one side of the equals sign and everything else is on the other side. Use either the point slope form or slope intercept form equation and work out the math to rearrange the equation into standard form. Note that the equation should not include fractions or decimals, and the x coefficient should only be positive.

Draw a straight line through those points that represent the graph of this equation. The number lines are called axes. Hence, the solution is the other half-plane.

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We have graphed linear equations by plotting points, using intercepts, recognizing horizontal and vertical lines, and using the point—slope method. Substituting into the slope formula:. The equation of this line is:. To find the slope of the line, we need to choose two points on the line. In Understand Slope of a Line , we graphed a line using the slope and a point. This equation is not in slope—intercept form. Not all linear equations can be graphed on this small grid. Now that we have seen several methods we can use to graph lines, how do we know which method to use for a given equation? While we could plot points, use the slope—intercept form, or find the intercepts for any equation, if we recognize the most convenient way to graph a certain type of equation, our work will be easier.

3x 2y 16 in slope intercept form

When you graph linear equations, you may notice that some lines tilt up as they go from left to right and some lines tilt down. Some lines are very steep and some lines are flatter. In mathematics, the measure of the steepness of a line is called the slope of the line. The concept of slope has many applications in the real world. In construction the pitch of a roof, the slant of the plumbing pipes, and the steepness of the stairs are all applications of slope. We can assign a numerical value to the slope of a line by finding the ratio of the rise and run. The rise is the amount the vertical distance changes while the run measures the horizontal change, as shown in this illustration. Slope is a rate of change. The rise measures the vertical change and the run measures the horizontal change.

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This fact will be used here even though it will be much later in mathematics before you can prove this statement. Write your answer If we write the slope as , then from the point 0,4 we move one unit in the positive direction parallel to the x-axis and then move three units in the negative direction parallel to the y-axis. Trending Questions. Note that -1 is the x value of the ordered pair given. No matter how far these lines are extended, they will never intersect. If you simplify the point slope equation above you get the equation of the line in slope intercept form. Slope Calculator - Two Points. All rights reserved. This is done by first multiplying each side of the first equation by You may want to review that section. Independent equations have unique solutions.

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Solution First we recognize that the equation is not in the slope-intercept form needed to answer the questions asked. Find the numbers. Click to expand Get the two equations for the lines into slope-intercept form. We will try 0, 1,2. First locate the point 0, When you have 2 points on a line on a graph the slope is the change in y divided by the change in x. Solution Placing the equation in slope-intercept form, we obtain Sketch the graph of the line on the grid below. So now the slope is 15? Solve equations and inequalities Simplify expressions Factor polynomials Graph equations and inequalities Advanced solvers All solvers Tutorials. Step 2: Identify the slope and y -intercept of the linear equation. To graph the solution to this system we graph each linear inequality on the same set of coordinate axes and indicate the intersection of the two solution sets. Find slope by finding the difference in the y points, and divide that by the difference in the x points. What is 3x-6y equals 9 in slope intercept form?