3x 2y 16 in slope intercept form

Step 3: Plot the y -intercept point on the graph.

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3x 2y 16 in slope intercept form

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. Note that this concept contains elements from two fields of mathematics, the line from geometry and the numbers from algebra. Rene Descartes devised a method of relating points on a plane to algebraic numbers. This scheme is called the Cartesian coordinate system for Descartes and is sometimes referred to as the rectangular coordinate system. Perpendicular means that two lines are at right angles to each other. The number lines are called axes. The horizontal line is the x-axis and the vertical is the y-axis.

We now wish to discuss an important concept called the slope of a line.

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.

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.

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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Continue Learning about Other Math. Now the slope is 1. Three times the first number added to five times the second number is 9. Example 2 Solve by addition:. Graphs are used because a picture usually makes the number facts more easily understood. Independent equations The two lines intersect in a single point. The horizontal line is the x-axis and the vertical is the y-axis. The slope is 0 and the y-intercept is Since the graph of a first-degree equation in two variables is a straight line, it is only necessary to have two points. As a check we substitute the ordered pair 3,4 in each equation to see if we get a true statement. Positive is to the right and up ; negative is to the left and down.

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To solve a system of two linear equations by graphing, graph the equations carefully on the same coordinate system. By continuing to use this site, you are consenting to our use of cookies. A common error that many students make is to confuse the y-intercept with the x-intercept the point where the line crosses the x-axis. New posts. Step 3 Solve for the unknown. It is the point where the line crosses the y axis. Usually, equations are written so the first term is positive. Since we have already solved the second equation for x in terms of y, we may use it. Equations in two unknowns that are of higher degree give graphs that are curves of different kinds. These values are arbitrary. A linear inequality graphs as a portion of the plane. Hi, I'm doing this exercise. Make a table of values and sketch the graph of each equation on the same coordinate system.