Answer:
Part 1) The number in the blank box is [tex]2[/tex]
Part 2) The slope of the line h is [tex]m=2[/tex]
Part 3) The equation of the line h is [tex]y=2x+4[/tex]
Step-by-step explanation:
Statement A
we know that
If two lines are perpendicular, the product of their slopes is equal to -1
so
m1*m2=-1
In this problem we have
[tex]m1=-\frac{1}{2}[/tex]
substitute in the formula and solve for m2
[tex]-\frac{1}{2}*m2=-1[/tex]
Multiply by -2 both sides
[tex]m2=2[/tex]
Statement B
we know that
The line h is perpendicular to the line g
therefore
The slope of the line h is equal to [tex]m=2[/tex]
Statement C
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where m is the slope
b is y-coordinate of the y-intercept
Find the equation of the line h
we have
[tex]m=2[/tex]
[tex]b=4[/tex] -----> observing the graph
substitute the values
[tex]y=2x+4[/tex]
