Question

Which equation represents the line that passes through points B and C on the graph? On a coordinate plane, point A is at (1, 4), point B is at (negative 4, 2), point C is at (negative 2, negative 2) and point D is at (5, negative 4). y = negative 2 x minus 6 y = negative 2 x + 10 y = 2 x minus 6 y = 2 x + 10

Answer 1

Answer:

y=negative 2x minus 6

Step-by-step explanation:

y-2= ((-2-2)/ (-2+4))(x+4)

y-2=(-4/2)(x+4)

y-2= -2(x+4)

y-2= -2x-8

y+2x=(-6)

y= -2x-6

Answer 2

Given:

Coordinates of four points A, B, C and D in which point A is at (1, 4), point B is at (-4, 2), point C is at (-2, -2) and point D is at (5, -4).

To find:

The equation of the line that crosses through points B and C on the graph.

Solution:

First of all, we need to find the slope of the line that crosses the two points B(-4, 2) and C(-2, -2).

Hence, the slope of the line that crosses two points (x, y) and (p, q) is given by:

$m = \frac{q - y}{p - x}$

Putting the value of coordinates of B(-4, 2) and C(-2, -2), we have

$m = \frac{ - 2 - 2}{ - 2 - ( - 4)} = \frac{ - 4}{2} = - 2$

Now, the equation of a line having slope 'm' and crosses a point (p, q) is given by:

$y - q = m (x - p)$

Using point B(-4, 2) and putting m = -2 in the above, we have

$y - 2 = -2 [x - (-4)]$

$y - 2 = -2 (x + 4)$

$y - 2 = -2x - 8)$

$y = -2x - 6$

Hence, the equation of the line that crosses points B and C on the graph is y = -2x - 6.

The correct option is y = -2x - 6.