we have
[tex]y=13x-2[/tex]
Statements
case A) The graph is a straight line.
The statement is True
Because, this is a linear equation of the form [tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
In this problem
[tex]m=13\ b=-2[/tex]
case B) The line passes through the origin
The statement is False
Because the point [tex](0,0)[/tex] is not a solution of the linear equation
Verify
Substitute the values of [tex]x=0[/tex] and [tex]y=0[/tex] in the equation
[tex]0=13*0-2[/tex]
[tex]0=-2[/tex] -------> is not true (the point not lie on the line)
case C) The line passes through the point [tex](0,-2)[/tex]
The statement is True
Because the point [tex](0,-2)[/tex] is a solution of the linear equation
Verify
Substitute the values of [tex]x=0[/tex] and [tex]y=-2[/tex] in the equation
[tex]-2=13*0-2[/tex]
[tex]-2=-2[/tex] -------> is true (the point lie on the line)
case D) The slope of the line is [tex]3[/tex]
The statement is False
Because the slope of the line is [tex]m=13[/tex]
case E) The y-intercept of the line is [tex]2[/tex]
The statement is False
Because
we know that
The y-intercept is the value of y when the value of x is equal to zero
Substitute the value of [tex]x=0[/tex] in the equation and find the value of y
[tex]y=13*0-2[/tex]
[tex]y=-2[/tex]
therefore
the y-intercept of the line is [tex]-2[/tex]
the answer is
The graph is a straight line.
The line passes through the point [tex](0,-2)[/tex]
see the attached figure to better understand the problem
