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

Question

Ethan Adkins · Accepted Answer

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#: #27/3 - 28/3 = b# #b = -1/3# #y = 4/3x - 1/3#

Genesis Allen · Answer

undefined To write the equation of a line in point-slope form and slope-intercept form given two points, follow these steps:

1. Find the slope using the formula $ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $, where $ (x_1, y_1) = (4, 5) $ and $ (x_2, y_2) = (7, 9) $.
2. Once you have the slope, choose one of the given points. Use the point-slope form: $ y - y_1 = m(x - x_1) $, where $ (x_1, y_1) $ is the chosen point and $ m $ is the slope.
3. Simplify the equation to slope-intercept form $ y = mx + b $ by isolating $ y $.

Let's calculate the slope first:

$$ m = \frac{{9 - 5}}{{7 - 4}} $$
$$ m = \frac{4}{3} $$

Now, choose one of the points, let's say (4, 5), and substitute into the point-slope form:

$$ y - 5 = \frac{4}{3}(x - 4) $$

Next, simplify the equation to slope-intercept form:

$$ y - 5 = \frac{4}{3}x - \frac{16}{3} $$
$$ y = \frac{4}{3}x - \frac{16}{3} + 5 $$
$$ y = \frac{4}{3}x - \frac{16}{3} + \frac{15}{3} $$
$$ y = \frac{4}{3}x - \frac{1}{3} $$

So, the equation of the line in point-slope form is $ y - 5 = \frac{4}{3}(x - 4) $, and in slope-intercept form, it is $ y = \frac{4}{3}x - \frac{1}{3} $.

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

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