MHB What is the slope and intercept in slope-intercept form?

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Slope-intercept form is represented by the equation y = mx + c, where m is the slope and c is the y-intercept. Understanding this form is crucial for working with scatter plots and lines of best fit, as it lays the foundation for more advanced mathematical concepts. For example, if a line has a slope of -3 and passes through the point (2, 12), the y-intercept can be calculated to find the complete equation. A video from Khan Academy provides further explanation on this topic. Mastering slope-intercept form enhances comprehension of linear equations and their applications in various mathematical contexts.
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I never quite understood slope-intercept form, my math teacher never really explained it too well. And so it kind of affects almost everything else I do. Like the scatter plots and lines of best fit sort of thing.
And all the more advanced stuff I never understood when I was in advanced classes.
 
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TheLibraSign said:
I never quite understood slope-intercept form, my math teacher never really explained it too well. And so it kind of affects almost everything else I do. Like the scatter plots and lines of best fit sort of thing.
And all the more advanced stuff I never understood when I was in advanced classes.

Are you familiar with writing linear equations any other way? For example $$ax+by+c = 0$$



Here's a video from Khan Academy about slope-intercept form.

Slope-intercept form is an equation in the form $$y = mx + c$$.

$$m$$ is the slope of the line and $$c$$ is the y intercept (shortened to intercept in the title).

Suppose you have the line $$y = x+1$$ which looks like this). The slope is 1 and the intercept is also 1.



For a different example suppose you know the slope of a line is -3 and it passes through the point (2,12). Immediately you can tell that $$m = -3$$.

To find the intercept you can plug in x=2 and y=12 into your equation and find $$c$$ -- $$12 = -3(2) + c \ \rightarrow c = 18$$

Thus the equation is $$y = -3x + 18$$
 
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