# how to find the equation of a line

What about given a slope and an intercept in y? Assuming a given straight line in the form of mx + b, any parallel line would have the same form with the same "m" but a different "b.". This article has been viewed 810,340 times. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. In either case, finding the equation for that line isn't difficult, provided you use the correct formula and work carefully. This article has been viewed 810,340 times. A "system" consists of at least two different equations (and thus at least two lines on a graph). The slope is undefined ... and where does it cross the Y-Axis? What is the equation for a vertical line. The final equation for a line in slope-intercept form with a slope of 2 that contains the point (4, 3) is, In this example, if you chose (3, 8) as your coordinates, then the formula would read, In our example, the formula currently reads 8 = 1(3)+b. \[{m_{AB}} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{6 - 0}}{{1 - ( - 2)}} = \frac{6}{3} = \frac{2}{1} = 2\]. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. ", doing these type of calculations. It, "I love the fact that it explains in a step-by-step method, as it's so easy to be bogged down with choices while, "Finally going back to school after 2 years, and this was very helpful to remember and refresh my math skills. Math Teacher. Different Countries teach different "notation" (as sent to me by kind readers): ... but it all means the same thing, just different letters. Grace Imson is a math teacher with over 40 years of teaching experience. helped me complete my MyMaths problems and to produce a set of revision notes about equations of lines. Interpreting a trend line. If you know two points that a line passes through, this page will show you how to find the equation of the line. If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. Finding the equation for a line is a common problem in geometry and trigonometry.

The equation of a straight line is usually written this way: y = mx + b (or "y = mx + c" in the UK see below) What does it stand for? The first way is to solve for the equation of a line with one {\displaystyle (x,y)} point and the equation of a line that runs perpendicular to it. The equation of a straight line can be written in many other ways. Last Updated: October 8, 2020 Our team of exam survivors will get you started and keep you going. Check for yourself that x=1 and y=3 is actually on the line.

It made a lot of sense, and it clicked in my brain. Then, plug the slope into the slope-intercept formula, or y = mx + b, where "m" is the slope and "x" and "y" are one set of coordinates on the line. Find the equation of the line with gradient 3, passing through (4, 1). This gives us divided by, or. The equation of a straight line is usually written this way: (or "y = mx + c" in the UK see Another popular form is the Point-Slope Equation of a Straight Line. Radio 4 podcast showing maths is the driving force behind modern science. This leaves you with 5 = b, or, For example, the equation for the line with points on (3, 8) and (7, 12) is. "The article led you through each method clearly, step by step, with picture examples and simple explanations. We can find the equation of a straight line when given the gradient and a point on the line by using the formula: where \(m\) is the gradient and \((a,b)\) is on the line. Find the equation of the line which passes through the points A(-2, 0) and B(1, 6) and state the gradient and y-intercept. References.

There are two common situations where you are asked to find the equation for a line: either you'll be provided with one point on the line and the slope of the line, or you'll be provided two points on the line. below), m = Slope or Gradient (how steep the line is), ... choose any value for x and find the matching value for y. Boost your career: Improve your Zoom skills. Next, we just need to find, which is the line's -intercept. If the equation holds true with those x and y values inserted, the point is on the line. y = x 3 Top marks. Interpreting a trend line. Method 1 ", "In 8th grade, you need stuff like this to help you when the teacher doesn't. Practice: Interpreting slope and y-intercept for linear models.

In this case, your slope, or m, equals 1. As the above article explains, two pieces of information are required in order to define a straight line: the line's slope and a point on the line. We have been looking at the "slope-intercept" form. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. Since we are given 2 points that already lie on the line, using the formula as before, we need to calculate the gradient first. To find the equation of a line using 2 points, start by finding the slope of the line by plugging the 2 sets of coordinates into the formula for slope. Practice: Estimating equations of lines of best fit, and using them to make predictions. Every point on the line has x coordinate 1.5, This is the currently selected item.

1 November 2019. Thank you, wikiHow! Now we can use the formula when m = 2, a = 1 and b = 6 (You can use any of the 2 points given in the question). Find the equation of the normal line to the curve y = x 3 at the point (2, 8). that is why its equation is x = 1.5. If you don't know the slope, you could have an infinite number of lines passing through a given point.

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