We can 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)(9/7)) = color(blue)(5/7)(x - color(red)(3/5))#
If required, we can solve for #y# to put this equation in the 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)(9/7) = (color(blue)(5/7) * x) - (color(blue)(5/7) * color(red)(3/5))#
#y - color(red)(9/7) = 5/7x - (color(blue)(color(black)(cancel(color(blue)(5)))/7) * color(red)(3/color(black)(cancel(color(red)(5)))))#
#y - color(red)(9/7) = 5/7x - 3/7#
#y - color(red)(9/7) + 9/7 = 5/7x - 3/7 + 9/7#
#y - 0 = 5/7x + 6/7#
#y = color(red)(5/7)x + color(blue)(6/7)#
