Question

3. Which statements about the line that passes through (-2, 0) and (2, -4) are true?

Select all that apply.
А The slope of the line is 1.
B The line intersects the y-axis at (0, -2).
C The equation of the line is y= -x-2
D The line intersects the x-axis at (-2, 0).

Answer 1

Answer: B, C, D

A is not True:
m = (y2 - y1) / (x2 - x1); Slope Formula
m = (-4 - 0) / (2 - (-2)); Plug in Values & Subtract
m = -4 / 4
m = - 1
m does NOT equal 1, so A is FALSE

B is True:
y = mx + b; Y-intercept Form equation
Choose one of the two coords and place in value for the equation— I chose (2, -4). m is the slope, which we know from solving A
-4 = -1(2) + b; multiply
-4 = -2 + b; add 2 both side
-2 = b
b is y-intercept or where the line hits the y-axis when x is 0– (0, -2), so B is TRUE

C is True:
y = mx + b; Place in Values for m (slope) and b (y intercept)
y = -1x - 2 or y = -x-2; so C is TRUE

D is True:
To find x intercept, set y to 0 and solve for x
y = mx + b
0 = -1(x) -2; multiply -1 & x; add 2 both side
2 = -x; divide both side by -1
-2 = x
This means when y is 0, x is at -2
(-2, 0); so D is TRUE

Answer 2

B, C, and D.

Explanation:

Let's go through each answer choice.

A: To find the slope of a line from two points, we use this formula:
`(y_2-y_1)/(x_2-x_1)`. Plugging in the values (-2,0) and (2, -4), we get:

• 
  `(-4-0)/(2+2)`

• 
  `-4/4`
• 
  `-1`

Because option A says the slope is 1, but we got -1, option A is false.

B: To find the y-intercept, we use this formula:
`b = y_1 - m * x_1`

• 
  `b = 0 -(-1) * (-2)`

• 
  `b = 1 * (-2)`

• 
  `b = -2`

Since we know the value of b is the y-intercept, we could write the y-intercept as (0,-2). Therefore, option B is true.

C: The equation of a line (in slope-intercept form) is y = mx + b, where y - y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. Since we already solved for the y-intercept and slope, let's plug in those values:

• 
  `y = mx +b`
• 
  `y = -x -2`

As you can see, the equation we got here matches the one in option C, meaning it's true.

D: We know that a point is written like this: (x, y). If the x-coordinate is not zero but the y-coordinate is, then it's the x-intercept. Since the question says that (-2,0) is one of the points the line passes through, and option D says that the x-intercept is (-2,0), it's true.