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

[TheLibraSign]

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.

 

[SuperSonic4]

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 $$ax+by+c = 0$$

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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.

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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 $$y = -3x + 18$$