How do you find the slope of the line that passes through (2.5,3), (1,-9)?

1 Answer
Mar 21, 2018

Slope (m): #color(blue)(=8#

Equation of the line passing through the points #color(red)((2.5, 3),(1,-9)# is given by

#color(blue)(y=8x-17)#

Explanation:

Given:

We are given the two points #color(red)((2.5, 3),(1,-9)#

These points are #color(blue)((x_a,y_1), (x_2,y_2)#

Slope-Intercept form of the equation of the line is

#color(green)(y = mx+b #, #color(red)(m# being the Slope.

We must find the values of #color(brown)(a and b)# to write the equation of the line.

Slope formula #color(blue)((m)= (y_2-y_1)/(x_2-x_1)#

#m=(-9-3)/(1-2.5)=8#

Substitute this value of #color(red)(m=8# in #color(blue)(y = mx+b#, using the point#color(green)((1,-9).#

We get,

#-9=8*1+b#

#-9=8+b#

Add #color(red)((-8)# to both sides of the equation.

#-9+color(red)((-8))=8+b+color(red)(-8#

#-9+color(red)((-8))=cancel(8)+b+color(red)(-cancel(8)#

#-17=b#

Hence,

#b=-17#. Observe that this is the y-intercept of the line.

Use the value of the slope #(m) = 8# and #b=-17# to obtain the equation of the line passing through the two points, in #y = mx+b#

We get,

#color(blue)(y = 8x-17#

Hence,

Equation of the line passing through the points #color(red)((2.5, 3),(1,-9)# is given by

#color(blue)(y=8x-17)#

Hope it helps.