Answer:
(-4, 17) and (5.-28)
(-6, 14) and (4.-16)
(-2.16) and (2.-20)
Step-by-step explanation:
we know that
If two lines intersect, then their slopes are different
The 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 line
points (-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 case
case 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 same
therefore
The lines not intersect because are parallel lines
case 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 same
therefore
The lines not intersect because are parallel lines
case 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 different
therefore
The 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 different
therefore
The 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 different
therefore
The lines intersect
