Q:

The line passing through the points (-2, 12) and (3, -23) intersects the line passing through which of these pairs of points? Select three that apply,(-3, 19) and (6.-44)(-5,32) and (3.-24)(-4, 17) and (5.-28)(-6, 14) and (4.-16)(-2.16) and (2.-20)

Accepted Solution

A:
Answer:(-4, 17) and (5.-28)(-6, 14) and (4.-16)(-2.16) and (2.-20)Step-by-step explanation:we know thatIf two lines intersect, then their slopes are differentThe formula to calculate the slope between two points is equal to[tex]m=\frac{y2-y1}{x2-x1}[/tex]Find the slope of the given linepoints (-2, 12) and (3, -23)substitute in the formula[tex]m=\frac{-23-12}{3+2}[/tex][tex]m=\frac{-35}{5}[/tex][tex]m=-7}[/tex]Verify each casecase 1(-3, 19) and (6.-44)substitute in the formula[tex]m=\frac{-44-19}{6+3}[/tex][tex]m=\frac{-63}{9}[/tex][tex]m=-7[/tex]Compare with the slope of the given line[tex]-7=-7[/tex]The slopes are the samethereforeThe lines not intersect because are parallel linescase 2(-5,32) and (3.-24)substitute in the formula[tex]m=\frac{-24-32}{3+5}[/tex][tex]m=\frac{-56}{8}[/tex][tex]m=-7[/tex]Compare with the slope of the given line[tex]-7=-7[/tex]The slopes are the samethereforeThe lines not intersect because are parallel linescase 3(-4, 17) and (5.-28)substitute in the formula[tex]m=\frac{-28-17}{5+4}[/tex][tex]m=\frac{-45}{9}[/tex][tex]m=-5[/tex]Compare with the slope of the given line[tex]-5 \neq -7[/tex]The slopes are differentthereforeThe lines intersect case 4(-6, 14) and (4.-16)substitute in the formula[tex]m=\frac{-16-14}{4+6}[/tex][tex]m=\frac{-30}{10}[/tex][tex]m=-3[/tex]Compare with the slope of the given line[tex]-3 \neq -7[/tex]The slopes are differentthereforeThe lines intersect case 5(-2.16) and (2.-20)substitute in the formula[tex]m=\frac{-20-16}{2+2}[/tex][tex]m=\frac{-36}{4}[/tex][tex]m=-9[/tex]Compare with the slope of the given line[tex]-9 \neq -7[/tex]The slopes are differentthereforeThe lines intersect