Linear Functions:Point - Slope Form

Given the slope of a line and a coordinate you can write a linear equation that is equivalent to the slope - intercept form.

y - y1 = m ( x - x1)

where (x1,y1) is a point on a nonvertical line with slope m..

Point - Slope Form of a Linear Equation

m = 4 point = (8,2)

y - y1 = m (x - x1) - point-slope form y - 2 = 4 ( x - 8) - substitute the values y - 2 = 4x - 32 - distribute the 4 +2 +2 - add 2 to both sides y = 4x - 30 - slope - intercept form

Example

You can also write a function rule given the coordinates of two points. First determine the slope of the line using the two points, and then write the equation by substituting one point and the slope into the point-slope form.

P1 (2, -3) and P2 (6, -1), write the equation of the line in slope-intercept form.

Find the slope: m = y2 - y1 = -1 - (-3) = 2 = 1 x2 - x1 6 - 2 4 2

Use the point-slope form, y - y1 = m (x - x1), and substitute m = ½ and one of the given points, (2, -3) or (6, -1).It doesn’t matter what point you use.

Example

P1 (2, -3)

y - y1 = m (x - x1) y - (-3) = ½ (x - 2) y +3 = ½ x - 1 -3 -3 y = ½ x - 4

P2 (6, -1)

y - y1 = m (x - x1) y - (-1) = ½ (x - 6) y +1 = ½ x - 3 -1 -1 y = ½ x - 4

Given the graph, determine the equation of the line in standard form.

Points: P1 (-2, 3), P2 (-1, -2)

Slope: m = y2 - y1 = -2 - 3 = -5 x2 - x 1 -1 - (-2) 1

y - y1 = m (x - x1) y - 3 = -5 (x - (-2)) y - 3 = -5x - 10 +3 +3 y = -5x -7 - slope intercept form 5x + y = -7 - standard form

Write the equation of the line in standard form. Indicate the y-intercept.

1. m = 3 through (5, 2)2. m = -⅖ throught (0,5)3. m = -6 through (30, 40)

You try!

Write in slope-intercept form.

4. y - 3 = 2(x -5)5. y + 7 = ½ (x - 1)6. y - 0 = -3(x + 8)