Question

QUESTION 1. Choose the point-slope form of the equation below that represents the line that passes through the points (−6, 4) and (2, 0). A) y − 4 = −one half(x + 6) B) y − 4 = 2(x + 6) C) y + 6 = −one half(x − 4) D) y + 6 = 2(x − 4) Question 2 (Multiple Choice Worth 2 points) Given the equation y − 3 = one half(x + 6) in point-slope form, identify the equation of the same line in standard form. A) x − 2y = −12 B) y = one halfx C) y = one halfx + 6 D) y = one halfx + 9

Answer 1

Answer:

First question: C) y + 6 = -1/2 ( x + 6)

Second question A) x - 2y = -12

Step-by-step explanation:

Question 1

First we calculate the slope:

m = (0-4)/(2+6) = (-4)/(8) = -1/2

Then we substitute in the formula

(y+6) = -1/2 (x+6)

Question 2

y - 3 = 1/2(x+6)

2(y-3) = x+6

2y -6 = x + 6

x - 2y = -12

Answer 2

Answer:

1. The correct answer is A.

2. The correct answer is A.

Step-by-step explanation:

1. The first step is to find the slope of the line. If we have the coordinates of two points that lie on the line we can use the formula

$m = \frac{y_2-y_1}{x_2-x_1}$,

where $m$ stands for the value of the slope, and the two points have coordinates $(x_1,y_1)$ and $(x_2,y_2)$.

Then, substituting (−6, 4) and (2, 0) we have

$m = \frac{0-4}{2-(-6)} = \frac{-4}{8} = -\frac{1}{2}.$

Recall that the point-slope equation of a line has the form

$y - y_1 = m(x-x_1)$

where $m$ stands for the slope and $(x_1,y_1)$ is any point of the line. Now, we found that $m = -\frac{1}{2}$ and taking the point $(x_1,y_1) = (-6,4)$, we substitute in the formula and obtain

$y-4 = -\frac{1}{2}(x+6)$.

Therefore, the point slope equation of the line is

$y-4 = -\frac{1}{2}(x+6).$

2. Recall that the standard equation of a line has the form $Ax+By =C$. Notice that only the equation in A. has this form. Anyway, let us check that, effectively, that A. is the correct answer.

The equation $y-3 = \frac{1}{2}(x+6)$ is equivalent to

$y-3 = \frac{1}{2}x+3$.

This equality is equivalent to

$-6 = \frac{1}{2}x-y$.

Now, multiplying the whole equation by 2, we obtain

$-12 = x-2y$.

The above identity is exactly the equation in A.