What is the equation of the line passing through #(4,8)# and #(-9,3)#?

Question

Kennedy Adams · Accepted Answer

point-slope form:
#y - 8 = frac{5}{13}(x-4)#
or
#y - 3 = frac{5}{13}(x+9)#

slope-intercept form:
#y = frac(5)(13)x + frac(84)(13)#

standard form:
#-5x + 13y = 84# Method 1: Use point slope form which is #y - y_1 = m(x - x_1)# when given a point #(x_1, y_1)# and the slope #m# ' In this case, we should first find the slope between the two given points. This is given by the equation: #m = frac{y_2 - y_1}{x_2 - x_1}# when given the points #(x_1,y_1)# and #(x_2, y_2)# ' For #(x_1,y_1) = (4,8)# and #(x_2,y_2) = (-9,3)# By plugging what we know into the slope equation, we can get: #m = frac{3-8}{-9-4} = frac{-5}{-13} = frac{5}{13}# ' from here we can plug in either point and get: #y - 8 = frac{5}{13}(x-4)# or #y - 3 = frac{5}{13}(x+9)# Method 2: Use slope intercept form which is #y = mx + b# when #m# is the slope and #b# is the y-intercept ' We can find the slope between the two given points using the same steps as above and get #m= frac{5}{13}# ' but this time when we plug in, we will still be missing the #b# or y-intercept to find the y-intercept, we need to temporarily plug in one of the given points in for #(x,y)# and solve for b ' so #y= frac{5}{13}x + b# if we plug in #(x,y)=(4,8)# we would get: #8 = frac(5)(13)(4) + b# ' solving for #b# would get us #8 = frac{20}{13} + b# #b = 84/13 or 6 frac(6)(13)# ' so your equation would be #y = frac(5)(13)x + frac(84)(13)# another form your equation could be in can be standard form where only the variables are on one side #ax + by = c# ' you can get you equation into this form by multiplying both sides of the slope intercept equation by 13 to get #13y = 5x + 84# then subtract #5x# from both sides ' so your standard form equation would be #-5x + 13y = 84#

Kennedy Adams · Answer

undefined The equation of the line passing through the points (4,8) and (-9,3) is y = (5/13)x + (89/13).

Jameson Allen · Answer

undefined To find the equation of the line passing through the points (4, 8) and (-9, 3), we first calculate the slope of the line using the formula:

$$ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $$

Substituting the coordinates of the points into the formula:

$$ m = \frac{{3 - 8}}{{-9 - 4}} $$

$$ m = \frac{{-5}}{{-13}} $$

$$ m = \frac{5}{13} $$

Now that we have the slope $ m = \frac{5}{13} $, we can use the point-slope form of the equation of a line:

$$ y - y_1 = m(x - x_1) $$

Using either of the given points, let's use (4, 8):

$$ y - 8 = \frac{5}{13}(x - 4) $$

To simplify, distribute $ \frac{5}{13} $ to $ x - 4 $:

$$ y - 8 = \frac{5}{13}x - \frac{20}{13} $$

Add 8 to both sides to isolate $ y $:

$$ y = \frac{5}{13}x - \frac{20}{13} + 8 $$

$$ y = \frac{5}{13}x - \frac{20}{13} + \frac{104}{13} $$

$$ y = \frac{5}{13}x + \frac{84}{13} $$

So, the equation of the line passing through the points (4, 8) and (-9, 3) is $ y = \frac{5}{13}x + \frac{84}{13} $.