How do you write an equation in point slope and slope intercept form given (4,5) & (7,9)?

Question

1624 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-04T17:03:03

Point-slope form: $y - 5 = 4/3 (x - 4)$

Slope intercept form: $y = 4/3x -1/3$

First find the slope $= m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2 - x_1)$ :

$m = (9-5)/(7-4) = 4/3$

Point-slope form $y - y_1 = m (x - x_1)$ :

$y - 5 = 4/3 (x - 4)$

To find the slope intercept form $y = mx + b$ :

Use the point-slope form and distribute: $y - 5 = 4/3x - 4/3 *4/1$

Simplify:

$y - 5 = 4/3x -16/3$

$y = 4/3x - 16/3 +5/1$

$y = 4/3x - 16/3 + 15/3$

$y = 4/3x -1/3$

Use slope and one point to find the $y$ -intercept $b$ :

#y = 4/3x + b#

#9 = 4/3 * 7/1 + b#

#9/1 = 28/3 + b#

$27/3 - 28/3 = b$

$b = -1/3$

$y = 4/3x - 1/3$