Writing Linear Equations Given Slope and a Point When you are given a real world problem that must be solved, you could be given numerous aspects of the equation. If you are given slope and the y-intercept, then you have it made. You have all the information you need, and you can create your graph or write an equation in slope intercept form very easily. However, most times it's not that easy and we are forced to really understand the problem and decipher what we are given.

What is the equation of this line in slope-intercept form? So any line can be represented in slope-intercept form, is y is equal to mx plus b, where this m right over here, that is of the slope of the line. And this b over here, this is the y-intercept of the line. Let me draw a quick line here just so that we can visualize that a little bit.

So that is my y-axis. And then that is my x-axis. And let me draw a line. And since our line here has a negative slope, I'll draw a downward sloping line.

So let's say our line looks something like that. So hopefully, we're a little familiar with the slope already.

The slope essentially tells us, look, start at some point on the line, and go to some other point of the line, measure how much you had to move in the x direction, that is your run, and then measure how much you had to move in the y direction, that is your rise.

And our slope is equal to rise over run. And you can see over here, we'd be downward sloping. Because if you move in the positive x direction, we have to go down.

If our run is positive, our rise here is negative. So this would be a negative over a positive, it would give you a negative number.

That makes sense, because we're downward sloping. The more we go down in this situation, for every step we move to the right, the more downward sloping will be, the more of a negative slope we'll have.

So that's slope right over here. The y-intercept just tells us where we intercept the y-axis. So the y-intercept, this point right over here, this is where the line intersects with the y-axis. This will be the point 0 comma b. And this actually just falls straight out of this equation.

When x is equal to so let's evaluate this equation, when x is equal to 0.

- Writing Linear Equations Given Slope and a Point
- Line (geometry) - Wikipedia

Well, anything times 0 is 0. So y is equal to 0 plus b, or y will be equal to b, when x is equal to 0. So this is the point 0 comma b. Now, they tell us what the slope of this line is.

Example 1: Writing an Equation Given Two Points |
Lines through a sphere A line can intersect a sphere at one point in which case it is called a tangent. It can not intersect the sphere at all or it can intersect the sphere at two points, the entry and exit points. |

Perpendicular Lines |
Find the slope and the y-intercept of the line. |

They tell us we go through the-- Let me just, in a new color. I've already used orange, let me use this green color. They tell us what we go through the point 0 comma 8.

Notice, x is 0. So we're on the y-axis. When x is 0, we're on the y-axis. So this is our y-intercept. So b, we could say-- we could do a couple-- our y-intercept is the point 0 comma 8, or we could say that b-- Remember, it's also 0 comma b.

We could say b is equal to 8. And we are done.In the last lesson, I showed you how to get the equation of a line given a point and a slope using the formula. Anytime we need to get the equation of a line, we need two things. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept..

If you know two points that a line passes through, this page will show you how to find the equation of the line. Equation of a Line from 2 Points. Here are two points (you can drag them) and the equation of the line through them. Explanations follow.

The Points. Put the slope and one point into the "Point-Slope Formula" 3. Simplify; Step 1: Find the Slope (or Gradient) from 2 Points.

Writing Algebra Equations Finding the Equation of a Line Given Two Points. We have written the equation of a line in slope intercept form and standard form. We have also written the equation of a line when given slope and a point.

Now we are going to take it one step further and write the equation of a line when we are only given two points that are on that line. Converting Equations to the Slope-Intercept Formula.

Let’s say we are given an equation in a form other than \(\boldsymbol{y=mx+b}\) and we were asked to graph ph-vs.com’s graph the line: \(x=7y+3\) We know that this equation is not in the slope-intercept form, and we must use what we’ve learned about algebra to somehow get it in the form we know.

Writing Linear Equations Given Slope and a Point. When you are given a real world problem that must be solved, you could be given numerous aspects of the equation. If you are given slope and the y-intercept, then you have it made. You have all the information you need, and you can create your graph or write an equation in slope intercept form very easily.

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