Slope-intercept form linear equations Video transcript - [Voiceover] There's a lot of different ways that you could represent a linear equation. So for example, if you had the linear equation y is equal to 2x plus three, that's one way to represent it, but I could represent this in an infinite number of ways. I could, let's see, I could subtract 2x from both sides, I could write this as negative 2x plus y is equal to three. I could manipulate it in ways where I get it to, and I'm gonna do it right now, but this is another way of writing that same thing.
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. While you could plot several points by just plugging in values of x, the point-slope form makes the whole process simpler.
Point-slope form is also used to take a graph and find the equation of that particular line. The point slope form gets its name because it uses a single point on the graph and the slope of the line.
Think about it this way: You have a starting point on a map, and you are given a direction to head. You have all the information you need to draw a single line on the map. The standard point slope formula looks like this: In this case it denotes a specific y value which you will plug into the equation.
The variable m is the slope of the line. Example 1 You are given the point 4,3 and a slope of 2. Find the equation for this line in point slope form.
Just plug the given values into your point-slope formula above. Your slope was given to you, so where you see m, use 2.
Your final result should look like: Your point is -1,5. Create the equation that describes this line in point-slope form.
Try working it out on your own.
If that's not what you got, re-read the lesson and try again. Point-slope form is all about having a single point and a direction slope and converting that between an algebraic equation and a graph.
In the example above, we took a given point and slope and made an equation. Now let's take an equation and find out the point and slope so we can graph it. Example 2 Find the equation in point-slope form for the line shown in this graph: To write the equation, we need two things: It is simple to find a point because we just need ANY point on the line.
The point I've indicated, -1,0just happens to be the easiest one to find. Note also that it is useful to pick a point on the axis, because one of the values will be zero. Finding the slope requires a little calculation, but it is also pretty easy. Just count the number of lines on the graph paper going in each direction of a triangle, like I've shown.
Therefore the slope of this line is 2. You could have used any triangle to figure out the slope and you would still get the same answer. Putting it all together, our point is -1,0 and our slope is 2.
We know how to use the point-slope form, so the final answer is: Check out this point-slope worksheetand when you're done, the answer key. As you can see, point-slope form is nothing too complicated. It is just one method to writing an equation for a line.
Just practice converting between a line on a graph and an equation and you'll get the hang of it in no time. And of course, if you need more help, feel free to ask the volunteers on our math help message board. Point-Slope Calculator Many functions to try!Rewrite the equation in slope-intercept form.
2. Identify the slope and y-intercept. Write and use a direct variation equation. 1. Write the direct variation equation. 2. Find the value of y when x = Compare Graphs of Linear Functions with the Graph of f(x) .
One way to determine the slope of a line, given its equation, is to change the equation to slope-intercept form, and then identify the coefficient of the x term. The coefficient of the x term is the slope of the line..
To write an equation in slope-intercept form, you must solve the equation for y.. Directions. The same can be said for a linear equation. There are various ways of writing a line, but they all describe the same line, as SparkNotes accurately states.
The form in which a linear equation is written will depend on the situation, but if you are ever asked to graph a line, then the Slope-Intercept Form is the one you want! Unit 6 Write Linear Equations Write Equations in Slope-Intercept Form Use Equations in Slope-Intercept Form Equations in Parallel/Perpendicular Form Fit Lines to Data.
Slope-Intercept Form Any linear equation can be written in the form 1=˘ +an equation in slope-intercept form, start by graphing the 1-intercept on the coordinate plane. From the 1-intercept, move the rise and run of the slope to plot another point.
line. This completes the. Circle the representation you used to answer this question. Is the slope of the line positive or negative? Equation.
Table: Graph. Verbal: When the x-value increases by 2, what happens to the y-value?. Equation.