An equation in the slope-intercept form is written as Show
$$y=mx+b$$ 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 The equation of a straight line is usually written this way: (or "y = mx + c" in the UK see below) What does it stand for?y = how far up x = how far along m = Slope or Gradient (how steep the line is) b = value of y when x=0 How do you find "m" and "b"?
m = Change in Y Change in X Knowing this we can work out the equation of a straight line:Example 1m = 2 1 = 2 b = 1 (value of y when x=0) Putting that into y = mx + b gets us: y = 2x + 1 With that equation we can now ... ... choose any value for x and find the matching value for y For example, when x is 1: y = 2×1 + 1 = 3 Check for yourself that x=1 and y=3 is actually on the line. Or we could choose another value for x, such as 7: y = 2×7 + 1 = 15 And so when x=7 you will have y=15 Positive or Negative Slope?Going from left-to-right, the cyclist has to Push on a Positive Slope:
Example 2m = −3 1 = −3 b = 0 This gives us: y = −3x + 0 We do not need the zero! So: y = −3x Example 3: Vertical LineWhat is the equation for a vertical line? In fact, this is a special case, and we use a different equation, not "y=...", but instead we use "x=...". Like this: x = 1.5 Every point on the line has x coordinate 1.5, Rise and RunSometimes the words "rise" and "run" are used.
And so the slope "m" is: m = rise run You might find that easier to remember. Other FormsWe have been looking at the "slope-intercept" form. The equation of a straight line can be written in many other ways. Another popular form is the Point-Slope Equation of a Straight Line. 358,359,517,518, 1156, 1157, 3204, 3205, 3206, 3207 FootnoteCountry Note:Different Countries teach different "notation" (as sent to me by kind readers):
... but it all means the same thing, just different letters. How do you find the linear function from a graph?Writing Linear Functions From a Graph. Find the slope by measuring the rise and run of the linear function.. Find the y-intercept by identifying where the function crosses the y-intercept.. Substitute the slope and y-intercept into the function.. How do you find an equation from a graph?Steps to find the equation of a line from two points:. Find the slope using the slope formula. ... . Use the slope and one of the points to solve for the y-intercept (b). ... . Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.. How do you find the equation of a linear relation on a graph?The equation of a linear relationship is y = mx + b, where m is the rate of change, or slope, and b is the y-intercept (The value of y when x is 0).
How do you find linear equations?The slope-intercept form of a linear equation is y = mx + b. In the equation, x and y are the variables. The numbers m and b give the slope of the line (m) and the value of y when x is 0 (b). The value of y when x is 0 is called the y-intercept because (0,y) is the point at which the line crosses the y-axis.
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How to find a linear equation from a graph
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