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.
