Point Slope Solution
We can use the point slope formula to write and equation for this line. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #(color(red)(x_1, y_1))# is a point the line passes through.
Substituting the slope and values from the point in the problem gives:
#(y - color(red)(29/10)) = color(blue)(14/25)(x - color(red)(12/5))#
Slope-Intercept Solution
We can also use the slope-intercept formula to write and equation for the line. 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 from the problem for #color(red)(m)# and the values from the point in the problem for #x# and #y# and solve for #color(blue)(b)#:
#29/10 = (color(red)(14/25) * 12/5) + color(blue)(b)#
#29/10 = 168/125 + color(blue)(b)#
#29/10 - color(red)(168/125) = 168/125 - color(red)(168/125) + color(blue)(b)#
#(25/25 xx 29/10) - (2/2 xx color(red)(168/125)) = 0 + color(blue)(b)#
#725/250 - 336/250 = 0 + color(blue)(b)#
#389/250 = color(blue)(b)#
Substituting the slope from the problem and the #y#-intercept we calculated into the formula gives:
#y = color(red)(14/25)x + color(blue)(389/250)#
