Using Slope and y-Intercept to Graph Lines
Point-slope and slope-intercept form from two points - Algebra I - Khan Academywhat the watch with
This online calculator can find and plot the equation of a straight line passing through the two points. The calculator will generate a step-by-step explanation on how to obtain the result. So we have:. Welcome to MathPortal. I designed this web site and wrote all the lessons, formulas and calculators. If you want to contact me, probably have some question write me using the contact form or email me on.
How-To Examples. You've probably already seen the basic method for graphing straight lines; namely , make a T-chart, plot some points, put your ruler against them, and draw the line. Given two points x 1 , y 1 and x 2 , y 2 , the formula for the slope of the straight line going through these two points is:. Slope-Intercept Form. Note that which point we pick as the "first" point is irrelevant; if we pick the other point to be "first", the subtractions will be reversed, but we'll still get the exact same value for the slope:. If you're not sure that the two formulas above give exactly the same values, no matter what pair of points is plugged into them, then pick some points and try them out. See what you get.
Many students find this useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y -intercept can easily be identified or read off from this form. So our next goal is to somehow figure out what the value of b first. Again, the value of y -intercept b is not directly provided to us. But we can utilize the given slope and a point to find it. Substitute the known values into the slope-intercept formula, and then solve for the unknown value of b.
The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will.
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In the previous lesson, you learned how to graph points on the coordinate plane. We can connect two points with a straight line. To graph the equation of a line, we plot at least two points whose coordinates satisfy the equation, and then connect the points with a line. We call these equations " linear " because the graph of these equations is a straight line. There are two important things that can help you graph an equation, slope and y-intercept. Slope We're familiar with the word "slope" as it relates to mountains.
Any straight line in Cartesian coordinates — the graphing system you're used to — can be represented by a basic algebraic equation. Even if you aren't handed these two pieces of information, you can use other data — like the location of any two points on the line — to figure it out. Imagine that you've been asked to write the slope-intercept equation for a line that passes through the points -3, 5 and 2, Calculate the slope of the line. This is often described as rise over run, or the change in the y coordinates of the two points over the change in x coordinates. So, given the two points in the example, you arbitrarily choose one of the points to be the first point in the line, leaving the other to be the second point.
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How do find the x and y intercepts and graph