Slope-intercept form linear equations Video transcript So you may or may not already know that any linear equation can be written in the form y is equal to mx plus b. Where m is the slope of the line. The same slope that we've been dealing with the last few videos.
We will assign a number to a line, which we call slope, that will give us a measure of the "steepness" or "direction" of the line.
It is often convenient to use a special notation to distinguish between the rectan- gular coordinates of two different points. We can designate one pair of coordinates by x1, y1 read "x sub one, y sub one"associated with a point P1, and a second pair of coordinates by x2, y2associated with a second point P2, as shown in Figure 7.
Note in Figure 7. The ratio of the vertical change to the horizontal change is called the slope of the line containing the points P1 and P2. This ratio is usually designated by m. Thus, Example 1 Find the slope of the line containing the two points with coordinates -4, 2 and 3, 5 as shown in the figure at the right.
Solution We designate 3, 5 as x2, y2 and -4, 2 as x1, y1. Substituting into Equation 1 yields Note that we get the same result if we subsitute -4 and 2 for x2 and y2 and 3 and 5 for x1 and y1 Lines with various slopes are shown in Figure 7.
Slopes of the lines that go up to the right are positive Figure 7. And note Figure 7. However, is undefined, so that a vertical line does not have a slope.
In this case, These lines will never intersect and are called parallel lines. Now consider the lines shown in Figure 7.
In this case, These lines meet to form a right angle and are called perpendicular lines. In general, if two lines have slopes and m2: If we denote any other point on the line as P x, y See Figure 7. In general let us say we know a line passes through a point P1 x1, y1 and has slope m. If we denote any other point on the line as P x, y see Figure 7.
In Equation 2m, x1 and y1 are known and x and y are variables that represent the coordinates of any point on the line. Thus, whenever we know the slope of a line and a point on the line, we can find the equation of the line by using Equation 2. Example 1 A line has slope -2 and passes through point 2, 4.
Find the equation of the line. The slope and y-intercept can be obtained directly from an equation in this form.
Example 2 If a line has the equation then the slope of the line must be -2 and the y-intercept must be 8. Solution We first solve for y in terms of x by adding -2x to each member.
We say that the variable y varies directly as x.
|General Form of Equation of a Line||Using the Point-Slope Form of a Line Another way to express the equation of a straight line Point-slope refers to a method for graphing a linear equation on an x-y axis. When graphing a linear equation, the whole idea is to take pairs of x's and y's and plot them on the graph.|
|Slope Intercept Form||Graphing a Linear Equation Using Slope Intercept Form Now that you've completed a lesson on graphing slope you are finally ready to graph linear equations. There are several different ways to graph linear equations.|
Example 1 We know that the pressure P in a liquid varies directly as the depth d below the surface of the liquid. In this section we will graph inequalities in two variables. That is, a, b is a solution of the inequality if the inequality is a true statement after we substitute a for x and b for y.
Thus, every point on or below the line is in the graph. We represent this by shading the region below the line see Figure 7.
· You can find the straight-line equation using the point-slope form if they just give you a couple points: Find the equation of the line that passes through the points (–2, 4) and (1, 2). I've already answered this one, but let's look at the initiativeblog.com://initiativeblog.com · Because we know only one point, we use (x, y) to represent any other initiativeblog.com-Slope Form of a Linear Equation S o far you have worked with linear equations in intercept form,y a bx.
When you know a line’s slope and y-intercept, you can write its equation directly in intercept initiativeblog.com Improve your math knowledge with free questions in "Point-slope form: write an equation from a graph" and thousands of other math initiativeblog.com://initiativeblog.com Algebra Examples.
Step-by-Step Examples. Algebra.
Linear Equations. Find the Equation Using Point-Slope Formula, Using the point-slope form, plug in,, and. Solve for. Tap for more steps Multiply by. Simplify the right side.
Tap for more steps Multiply initiativeblog.com://initiativeblog.com Slope Calculator. The slope or gradient of a straight line can be calculated when two co-ordinate points (x1,y1) and (x2,y2) are given.
A slope, also known as gradient describes the steepness of a initiativeblog.com://initiativeblog.com · There are several ways to write an equation of a line.
In this lesson you will use the point-slope form of a line to create a graph. You will investigate the relationship between perpendicular lines and adjust the calculator's Viewing Window so that the lines look perpendicular. Selecting 6 initiativeblog.com