We can first use the point-slope formula to write an equation for the line in the problem. 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)(5)) = color(blue)(3)(x - color(red)(2))#
Now, solve for #y# to put the formula in slope-intercept form. 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.
#y - color(red)(5) = (color(blue)(3) xx x) - (color(blue)(3) xx color(red)(2))#
#y - color(red)(5) = 3x - 6#
#y - color(red)(5) + 5 = 3x - 6 + 5#
#y - 0 = 3x - 1#
#y = color(red)(3)x - color(blue)(1)#
