First, we need to determine the slope. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.
Substituting the values from the points in the problem gives:
#m = (color(red)(4) - color(blue)(-1))/(color(red)(3) - color(blue)(-1)) = (color(red)(4) + color(blue)(1))/(color(red)(3) + color(blue)(1)) = 5/4#
The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.
We can substitute the slope for we calculated #m# and the values from one for the points for #x# and #y# and solve for #b#:
#y = color(red)(m)x + color(blue)(b)# becomes:
#4 = (color(red)(5/4) * 3) + color(blue)(b)#
#4 = color(red)(15/4) + color(blue)(b)#
#4 - 15/4 = color(red)(15/4) - 15/4 + color(blue)(b)#
#(4/4 * 4) - 15/4 = 0 + color(blue)(b)#
#16/4 - 15/4 = color(blue)(b)#
#1/4 = color(blue)(b)#
We can now substitute the slope and value for #b# we calculated into the formula to write the equation:
#y = color(red)(5/4)x + color(blue)(1/4)#
