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## Algebra (all content)

### Course: Algebra (all content)ย >ย Unit 3

Lesson 7: Writing slope-intercept equations- Slope-intercept equation from graph
- Writing slope-intercept equations
- Slope-intercept equation from graph
- Slope-intercept equation from slope & point
- Slope-intercept equation from two points
- Slope-intercept from two points
- Slope-intercept form problems
- Slope-intercept equation from slope & point (old)
- Slope-intercept equation from slope & point: fractions (old)
- Finding y intercept given slope & point (old)
- Slope-intercept form review

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# Slope-intercept equation from slope & point (old)

An old video where Sal finds the slope-intercept form of a line that has a slope of 7 and goes through the point (-4,-11). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- Doesn't the steepness of a slope depend on the marginal value of units on a given graph? So the steepness of a slope of (7) could be very steep (if numbered by units of one) or not steep at all (if numbered by units of 100). (I believe advertisers use this trick to fool people on rises and falls of certain markets)(15 votes)
- Mo,

The steepness would be the same no matter which units you use.

If you used units of 100, you would go over 100 and up 700.

In you used units of 1/10, you would go over 1/10 and up 7/10.

In fact, if the line goes through the origin, the points (1/10 , 7/10) and (100,700) would both be on the line. The steepness of the line would be a slope of 7.

The steepness of the line would be the exact same.

But, yes, advertisers and others do often use math misconceptions to mislead people.(20 votes)

- What is the m and what is the b in y=mx+b?(5 votes)
- m is the slope and b is the y-intercept.(8 votes)

- How does a linear equation become undefined. Can it go on forever, and can it be negative? Also, why is the y-axis undefined, but the x-axis is different. What is the reason behind that?(5 votes)
- Hi Amogh Mandava!

When finding the slope of a line using the slope formula (y2-y1/x2-x1), the slope of a vertical line would be (y/0). However, division by zero is undefined. Hence, the equation's slope is undefined. However, for a horizontal line, the slope formula would end up (0/x). A number divided by zero is zero. Thus, we can determine that a horizontal line's slope is 0.

slr(1 vote)

- So the answer to this question would be in equation form? And all we have to figure out is m and b, right?(4 votes)
- Hey! I haven't practiced math in over ten years and am now preparing for the GMAT. Your videos have been invaluable in the refreshing process: my memory thanks you. Actually, I have a number of friends that are currently preparing for the GMAT and they all use your videos. Keep it up!(5 votes)
- why couldn't a vertical line have a equation something like y=(ifinity/0)x+0 which I know a number divided by 0 is undefined I was just wandering if this would define a vertical line with an equation(1 vote)
- The problem isn't coming up with an equation. For example, the equation of a vertical line through the point (3,0) is x=3. The problem is that the slope of the line is undefined, because we get zero in the denominator of a fraction. It's natural to feel there's something unsatisfactory in this state of affairs and wonder if there might be some way around it, but in the end it's just a fact of life we have to accept.(3 votes)

- Is the equation y=mx+b interchangeable with x=my+b with "b" as the x intercept?(1 vote)
- No, the value of m and b will be different for most equations.(3 votes)

- How Would We Solve y=mx-2(1 vote)
- This is the equation of a line on a graph, to solve this you must realise, the equation can also be written as 1y=1m1x-2. Y= The location of the point on the Y axis. X= The location of the point on the X axis. M= The slope. -2= Is the Y intercept, If there is a graph you can replace X and Y with the real co-ordinates, Ex: X=3 Y=5 5=3x-2. I hope it helps, that's how I'd solve it. :D(3 votes)

- line t is perpendicular to line y=4x. what is the gradient of line t(1 vote)
- Perpendicular lines are the negative recipricol of your line that you have. So your line t equation should be y = -1/4x(2 votes)

- find the equation of a line that passes through (-6,3) and (2,5)(1 vote)
- Start by using the slope formula to find the slope of your line: m = (y2-y1)/(x2-x1)

Then, follow the steps shown in this video to get your equation. Give it a try.

If you want a video with a similar problem that starts with 2 points, see this link: https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func/alg-writing-slope-intercept-equations/v/equation-of-a-line-3(2 votes)

## Video transcript

A line has a slope of 7
and goes through the point negative 4, negative 11. What is the equation of this
line in slope-intercept form? So the equation of any line
in slope-intercept form is y is equal to mx plus
b, where m is the slope and b is the y-intercept. Now, in this problem right
here, they tell us the slope. They tell us that a
line has a slope of 7. So we know right from the
get go that m is equal to 7. So we know the equation of this
line in slope-intercept form is going to look like y is
equal to, we know m is 7, so 7x plus-- let me
make that x a little bit neater-- 7x plus b. And now what we need to do,
we need to figure out b, and they give us one more
piece of information. They say that the line goes
through the point negative 4 comma negative 11. So that tells us that when
x is equal to negative 4, then y is equal to negative 11. So we can use this
information in what we have or the part of our
equation that we've been able to figure out so far. We know that when x is
equal to negative 4, y is going to be
equal to negative 11. So what b do we need
to make that happen? Let's try it out. So y is negative 11 when
x is equal to negative 4. So negative 11 is equal to
7 times x-- and in this case x is negative 4-- plus b. And now we can just solve for b. A b that makes this
equation, or that satisfies the constraint that
when x is equal to negative 4, y is equal to negative 11. So let's see, we get negative 11
is equal to 7 times negative 4 is negative 28
plus b, and now we can add a 28 to both
sides of this equation. So let's add a 28. I'm just trying to isolate
the b on the right-hand side. And so on the left-hand
side, negative 11 plus 28, that is just positive 17. These guys cancel
out on purpose. And I just have a b on
the right-hand side. So I get b is equal to 17. Let me write it in green. That's not green. We get b is equal to 17. So we know m is 7, they told
us that right at the beginning. And now we know b is 17. So the equation of
our line is y is equal to 7x, that's our slope. 7 times x plus b,
and b here is 17. And if we wanted to graph it, it
would look something like this. I'll just do a real rough graph. So if we wanted to graph
this line, that's my x-axis, and this is my y-axis. The y-intercept is 17. So that means that the
point 0, 17 is on this line. So this point right over
here is going to be 0, 17. And our slope is 7. So that means if we move to the
right one, we move up t seven. So it's a high slope. So if we move to the right
one, we move up seven. Or if we move back one,
will move down seven. So we'll move down
seven, so the line will look roughly like this. Obviously, haven't
done it very exactly, but our line is
going to look like. That's going to be a pretty
steep upward-sloping line. It has a very high
slope, slope of seven. If you move one in
the x direction, you have to move up seven. And its y-intercept
is at y is 17. When x is 0, y is 17.