5.3 Write Linear Equations in Point-Slope Form

Big Idea: -Verify that a point lies on a line, given an equation of a line. -Derive linear equations by using the point-slope formula.

Previously you learned one strategy for writing a linear equation when Previously you learned one strategy for writing a linear equation when given the slope and a point on the line. In this lesson you will learn a given the slope and a point on the line. In this lesson you will learn a different strategy – one that uses the different strategy – one that uses the point-slope formpoint-slope form of an equation of an equation of a line.of a line.What we Know so far….What we Know so far….

Slope Intercept Form: y = mx + b

The New Stuff… Point- Slope The New Stuff… Point- Slope FormFormThe point-slope form of the equation of the nonvertical line through a The point-slope form of the equation of the nonvertical line through a given point with slope of given point with slope of mm is: is:

Again, where Again, where mm is the slope and is a point on the line. is the slope and is a point on the line.

y y1 m(x x1)(y1, x1)

(y1, x1)

Example: Write an equation in point-slope form.

• (1) Write an equation in point-slope form of the line that passes through the point (-1, 4) and has a slope of -2.

(2) Write an equation in point-slope form of the line that passes through the point (-3, 1) and has a slope of 3.

Using Point-Slope

Write an equation in point-slope form:

Find the slope of the line:

Write the equation in point-slope form. Use the point (2, 2):

Graph an equation in point-slope form:

• (1) Graph the equation y - 1 = -(x - 2)

(2) Graph the equation y 2 12

(x 2)

Write an equation in point-slope form of the line shown:

Find the slope of the line:

Write the equation in point-slope form. You can use either given point.

(1, 1)(-1, 3)

Example 2: Write in point-slope form:

Find the slope of the line:

Write the equation in point-slope form. You can use either given point.

(-2, 3)

(1, -3)

Extra Example:

• Write an equation in point-slope form of the line that passes through the points (2, 3) and (4, 4).