Question

To solve the equation 2x−3=3x−7 , Esin graphs the functions f(x)=2x−3 and g(x)=3x−7 on the same set of coordinate axes.

Which statement describes the solution of the equation ​ 2x−3=3x−7 ?


The solution of the equation cannot be found graphically. Esin should solve the equation algebraically.

The solution of the equation is the y-intercept of the linear equations.

The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.

The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect

Answer 1

we have that

f(x)=2x−3
g(x)=3x−7

2x-3=3x-7-------------> 3x-2x=-3+7-------> x=4 
find the value of f(x) or g(x) for x=4
f(x)=2x−3 ------->  f(4)=2*4-3------> f(4)=5
the solution is the point (4,5)

using a graph tool
see the attached figure

statement

case a) The solution of the equation cannot be found graphically. Esin should solve the equation algebraically.
this is not correct

case b) The solution of the equation is the y-intercept of the linear equations.
this is not correct

case c)The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.
this is correct

case d) The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect
this is not correct

the answer is 
case c) The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.