What's Point-Slope Form of a Linear Equation?

Summary

Point-slope form is one way of writing an equation of a line
'm' represents the slope
(x₁,y₁) is a point on the line
The slope, m, is -1
The point we know, (x₁,y₁), is (3,2)

Notes

1. The slope of a line is just it's steepness
2. It is represented by the variable 'm'
3. It can be found by dividing the change in y by the change in x, or by taking the rise over the run
1. x₁ and y₁ represent the coordinates of a point we know on the line
1. Point-slope form is one way of writing a linear equation
2. Linear equations can also be written in SLOPE-INTERCEPT form and STANDARD form
1. Point-slope form is one way of writing a linear equation
2. Linear equations can also be written in SLOPE-INTERCEPT form and STANDARD form
1. y₁ represents the y-coordinate of a point we know on the line
1. m represents the slope, or steepness, of the line
2. x₁ represents the x-coordinate of a point we know on the line
1. If we have the slope and a point, we can just plug the values we know into the formula
2. This will give us an equation for the line!
1. It's called POINT-SLOPE form because it's easy to work with if we have a POINT and the SLOPE
1. So m is equal to -1
1. (x₁,y₁) is (3,-2)
1. Since we know the slope and a point, we can use point-slope form to easily write an equation for the line
1. Our slope is -1
2. Our point is (3,-2)
3. So we can just plug these values into the formula y-y₁=m(x-x₁) to get our equation
1. m, our slope, is -1
2. (x₁,y₁), our point, is (3,-2)
1. We can plug -2 in for y₁ in the formula
1. We can plug -1 in for m in the formula
2. And we can plug 3 in for x₁
1. y--2 becomes y+2, since subtracting a negative is the same as adding a positive
1. This is just one form of the equation for this line
2. It could also be written in slope-intercept form or standard form
1. Point-slope form is the best form to use if you know the slope and a point

Definition: Point-Slope Form

Summary

Notes