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The line has a slope of negative 1 and contains the point 4/5 comma 0. The whole reason I did that is so that cancels out with that. So they haven't given us the slope or the y-intercept explicitly. The reason why I color-coded it is I wanted to show you when I used this y term first, I used the 6 up here, that I have to use this x term first as well. Then I would have gotten the negative of the answer. So let's say it's 0 minus 5 just like that. Now, we can use this coordinate information, the fact that it contains this point, we can use that information to solve for b. We could add 5/2 to both sides of the equation, plus 5/2, plus 5/2. So that's the coordinate if you imagine that y is equal to f of x. If I used these guys first, I would have to use both the x and the y first.
Since a vertical line goes straight up and down, its slope is undefined.
Also, the x value of every point on a vertical line is the same.
For whatever reason, there are different formats for simple linear equations.
I prefer the slope-intercept form; at times, the point-slope form is helpful; some textbooks strongly prefer what they sometimes call the "intercept" form, which is often (though not always) given as being " From what I've learned about slope, I know that parallel lines have the same slope, and perpendicular lines have slopes which are negative reciprocals (that is, which have opposite signs and which are flipped fractions of each other). These slopes have opposite signs, so their lines are not parallel.
But the slopes are the same fraction, rather than one being the flip (that is, the reciprocal) of the other, so these lines are not perpendicular, either.
$$slope=\frac=\frac$$ The slope of a line is usually represented by the letter m.
Just as a bit of a review, that means equations of lines in the form of y is equal to mx plus b where m is the slope and b is the y-intercept. So here they tell us that a line has a slope of negative 5, so m is equal to negative 5. So we know that this equation is going to be of the form y is equal to the slope negative 1x plus b, where b is the y-intercept. So we know that the slope m is equal to change in y over change in x, which is equal to-- What is the change in y?
The equation of this line is y is equal to negative 5x plus 6. So they're telling us the slope, slope of negative 1. But we could figure out both of them from these coordinates. So that's a 6-- I want to make it color-coded-- minus 0. So I wanted to show you, this is the coordinate 2 comma 6.
It's the same thing as the rise over the run, which is the same thing as the change in y over the change in x.
The equation is y-- let me do it in a new color-- y is equal to negative 2x plus b plus 10. Just like the last problem, we start by figuring out the slope, which we will call m.