Since the slope of the first line is 2, an equation of this line can be written in the form
y=2x+c,where c is the y-intercept of the line. Since the line contains the point
(1,8),one can substitute 1 for x and 8 for y in
y=2x+c, which gives
8=2(1)+c, or
c=6. Thus, an equation of the first line is
y=2x+6.The slope of the second line is equal to
or
−1.Thus, an equation of the second line can be written in the form
y=−x+d,where d is the y-intercept of the line. Substituting 2 for x and 1 for y gives
1=−2+d,or
d=3.Thus, an equation of the second line is
y=−x+3.
Since a is the x-coordinate and b is the y-coordinate of the intersection point of the two lines, one can substitute a for x and b for y in the two equations, giving the system
b=2a+6 and
b=–a+3. Thus, a can be found by solving the equation
2a+6=−a+3,which gives
a=−1. Finally, substituting
−1 for a into the equation
b=–a+3 gives
b=−(−1)+3, or
b=4.Therefore, the value of
a+b is
3.
Alternatively, since the second line passes through the points
(1,2) and
(2,1), an equation for the second line is
x+y=3. Thus, the intersection point of the first line and the second line,
(a,b) lies on the line with equation
x+y=3. It follows that
a+b=3Choices A and C are incorrect and may result from finding the value of only
a or
b,but not calculating the value of
a+b. Choice D is incorrect and may result from a computation error in finding equations of the two lines or in solving the resulting system of equations.