First, we can use the slope-intercept formula to find an equation for this 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.
Substituting the slope and y-intercept from the problem gives:
#y = color(red)(-1/3)x + color(blue)(10/3)#
Next, we need to transform to the standard form.
The standard form of a linear equation is:
#color(red)(A)x + color(blue)(B)y = color(green)(C)#
where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
#y = -1/3x + 10/3#
#color(red)(3) xx y = color(red)(3)(-1/3x + 10/3)#
#3y = (color(red)(3) xx -1/3x) + (color(red)(3) xx 10/3)#
#3y = (cancel(color(red)(3)) xx -1/color(red)(cancel(color(black)(3)))x) + (cancel(color(red)(3)) xx 10/cancel(color(black)(3))))#
#3y = -1x + 10#
#color(red)(1x) + 3y = color(red)(1x) - 1x + 10#
#1x + 3y = 0 + 10#
#color(red)(1)x + color(blue)(3)y = color(green)(10)#
