# Write an equation of the line satisfying the given conditions

Well, it's perpendicular to A, so it's going to be the negative inverse of this. So what we'll do is figure out the slope of A, then take the negative inverse of it. So the slope here is equal to 2. So we know that B's equation has to be y is equal to its slope, m times x plus some y-intercept. And its y-intercept we just figured out is negative 4. A positive y-intercept means the line crosses the y-axis above the origin, while a negative y-intercept means that the line crosses below the origin.

### Find the slope intercept form for the line satisfying the conditions

When the absolute value of m gets close to zero, the slope flattens. As m, the slope, gets larger, the line gets steeper. The slope of A is right there, it's the 2, mx plus b. And we are done. That's not a b there, that's a 6. A positive y-intercept means the line crosses the y-axis above the origin, while a negative y-intercept means that the line crosses below the origin. And its y-intercept we just figured out is negative 4. And they tell us that line A has an equation y is equal to 2x plus We still don't know what the y-intercept of B is, but we can use this information to figure it out. It's negative 3, is equal to negative 3 plus our y-intercept.

Let's add 3 to both sides of this equation, so if we add 3 to both sides-- I just want to get rid of this 3 right here-- what do we get? And they tell us that line A has an equation y is equal to 2x plus I just know that this is on the point, so this point must satisfy the equation of line B.

## Equation of a line

And its y-intercept we just figured out is negative 4. In this equation, x and y are coordinates of a point, m is the slope , and b is the y-coordinate of the y-intercept. So what we'll do is figure out the slope of A, then take the negative inverse of it. That's not a b there, that's a 6. So let's work out what b must be-- or what b, the y-intercept, this is a lowercase b, not the line B. You should have noticed that changing the value of m could swivel the line from horizontal to nearly vertical and through every slope in-between. I just know that this is on the point, so this point must satisfy the equation of line B.

Then we'll know the slope of B, then we can use this point right here to fill in the gaps and figure out B's y-intercept. And they tell us lines A and B are perpendicular, so that means that slope of B must be negative inverse of slope of A.

## Equation of a line

And we are done. You should have noticed that changing the value of m could swivel the line from horizontal to nearly vertical and through every slope in-between. When working with linear relationships, the slope-intercept form helps to translate between the graph of a line and the equation of a line. The left-hand side, negative 7 plus 3 is negative 4, and that's going to be equal to-- these guys cancel out-- that's equal to b, our y-intercept. Simply by changing the values of m and b, you can define any line. So what's the slope of A? And its y-intercept we just figured out is negative 4. It's negative 3, is equal to negative 3 plus our y-intercept. It has two slider bars that can be manipulated.

For this line, the slope isand the y-intercept is 4.

Rated 7/10 based on 26 review