Question

Examine these points on line u and line v. Line u: (9, –8), (5, 4) Line v: (4, 2), (7, –7) How many points of intersection are there between line u and line v? zero one two infinitely many.

Answer 1

There is no point of intersection between line u and line v.

Given that

These points on line u and line v.

Line u: (9, –8), (5, 4)

Line v: (4, 2), (7, –7)

We have to determine

How many points of intersection are there between line u and line v?

According to the question

To determine the point of intersection follows all the steps given below.

Line u: (9, –8), (5, 4)

The slope of the line u is,

$\rm Slope = \dfrac{4-(-8)}{5-9}\\\\Slope = \dfrac{4+8}{-4}\\\\Slope = \dfrac{12}{-3}\\\\Slope = -4$

And the value of c is at point (5, 4) is,

$\rm y = mx+c\\\\4= -3\times 5+c\\\\c = 4+15\\\\c=19$

The equation of u is y = -3x + 19.

And

Line v: (4, 2), (7, -7)

The slope of line V is,

$\rm Slope = \dfrac{-7-(2)}{7-4}\\\\Slope = \dfrac{-7-2}{3}\\\\Slope = \dfrac{-9}{3}\\\\Slope = -3$

And the value of c is at point (4, 2) is,

$\rm y = mx+c\\\\2= -3\times 4+c\\\\c = 2+12\\\\c=14$

The equation of u is y = -3x + 14.

The slopes of them are equal and their y-intercepted are not equal.

Line u is parallel to line v.

Hence, there is no point of intersection between line u and line v.

To know more about Slope click the link given below.

brainly.com/question/2514839