If you multiply the slopes of two perpendicular lines, the product is βˆ’1. (As long as neither line is vertical.) Use that fact and the graph to complete the statements below.

Accepted Solution

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 Awe know thatIf two lines are perpendicular, the product of their slopes is equal to -1som1*m2=-1In 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 Bwe know thatThe line h is perpendicular to the line gthereforeThe slope of the line h is equal to [tex]m=2[/tex]Statement Cwe know thatThe 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-interceptFind the equation of the line hwe have[tex]m=2[/tex][tex]b=4[/tex] -----> observing the graphsubstitute the values[tex]y=2x+4[/tex]