There are several forms that the equation of a line can take. They may look different, but they all describe the same line--a line can be described by many equations. All (linear) equations describing a particular line, however, are equivalent. Show The first of the forms for a linear equation is slope-intercept form. Equations in slope-intercept form look like this: where m is the slope of the line and b is the y-intercept of the line, or the y-coordinate of the point at which the line crosses the y-axis. To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y-intercept--this should be of the form (0, b). The y- coordinate is the value of b in the equation. Finally, write the equation, substituting numerical values in for m and b. Check your equation by picking a point on the line (not the y-intercept) and plugging it in to see if it satisfies the equation. Example 1: Write an equation of the following line in slope-intercept form: Graph of a Line First, pick two points on the line--for example, (2, 1) and (4, 0). Use these points to calculate the slope: m = =
= - . Example 4: Write an equation of the line with y-intercept 4 that is perpendicular to the line 3y - x = 9. The slope of 3y - x = 9 is . An equation in the slope-intercept form is written as $$y=mx+b$$ Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept. Example Find the equation of the line Choose two points that are on the line Calculate the slope between the two points $$m=\frac{y_{2}\, -y_{1}}{x_{2}\, -x_{1}}=\frac{\left (-1 \right )-3}{3-\left ( -3 \right )}=\frac{-4}{6}=\frac{-2}{3}$$ We can find the b-value, the y-intercept, by looking at the graph b = 1 We've got a value for m and a value for b. This gives us the linear function $$y=-\frac{2}{3}x+1$$ In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points. We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope $$m=-\frac{2}{3}$$ This gives us the equation $$y=-\frac{2}{3}x+b$$ From this we can solve the equation for b $$b=y+\frac{2}{3}x$$ And if we put in the values from our first point (-3, 3) we get $$b=3+\frac{2}{3}\cdot \left ( -3 \right )=3+\left ( -2 \right )=1$$ If we put in this value for b in the equation we get $$y=-\frac{2}{3}x+1$$ which is the same equation as we got when we read the y-intercept from the graph. To summarize how to write a linear equation using the slope-interception form you
Once you've got both m and b you can just put them in the equation at their respective position. Video lessonFind the equation to the graph How do you write an equation in slopeWe can write the slope-intercept equation from a graph. The point where the graph crosses the y-axis is our b-value. The slope is our m-value. Plug these into y=mx+b.
How do you write an equation from a graph?To find the equation of a graphed line, find the y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. Slope is the change in y over the change in x.
How do you find the equation in slopeThe slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.
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