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 Earlier in this chapter we have expressed linear equations using the standard form Ax + By = C and also y= mx +b. Now we're going to focus on the slope-intercept form y = mx + b. In the slope-intercept form you use the slope of the line and the y-intercept to express the linear function. $$y=mx+b$$ Where m is the slope and b is the y-intercept. Example
Graph the equation $$y-2x=1$$ rewrite in slope-intercept form $$y=2x+1$$ Identify the slope and the y-intercept m = 2 and b = 1 Plot the point corresponding to the y-intercept, (0,1) The m-value, the slope, tells us that for each step to the right on the x-axis we move 2 steps upwards on the y-axis (since m = 2) And once you have your second point you can just draw a line through the two points and extend it in both directions. You can check to see that the line you've drawn is the correct one by substituting the coordinates of the second point into the original equation. If the equation holds true than the second point is correct. Our second point = (1, 3) $$y-2x=1$$ $$3-2\cdot 1=3-2=1$$ Our second point is a solution to the equation i.e. the line we drew is correct. A line that passes through the origin has a y-intersect of zero, b = 0, and represents a direct variation. $$y=mx$$ In a direct variation the nonzero number m is called the constant of variation. You can name a function, f by using the function notion $$f\left ( x \right )=mx+b$$ f(x) is another name for y and is read as "the value of f at x" or "f of x". You can use other letters than f to name functions. A group of functions that have similar characteristics are called a family of functions. All functions that can be written on the form f(x) = mx + b belong to the family of linear functions. The most basic function in a family of functions is called the parent function. The parent function of all linear functions is $$f\left ( x \right )=x$$ Video lessonGraph y = 3x - 2 How do you graph a linear equation?To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.
What is a linear equation in slopeSlope intercept form is y=mx+b, where m is slope and b is the y-intercept. We can use this form of a linear equation to draw the graph of that equation on the x-y coordinate plane.
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How to graph a linear equation in slope intercept form
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