Question

multiple choice
identify the choice that best completes the statement or answers the question.

1. which of the following represents 4y - 2x = -20 in slope - intercept form?

a. y = -2x + 10
b. y = 2x - 10
c. y = -2x - 10
d. y = 2x + 10

1. m is the midpoint of ab. given a(-13, 9) and m(-2, 5), find the coordinates of b.

a. (12, 4)
b. (-17, 19)
c. (9, 1)
d. (-15/2, 7)

1. given the points x(-1, 2) and y(7, 14), find the coordinates of the point p on directed line segment xy that partitions xy in the ratio 1:3.

a. (1, 5)
b. (1, 1)
c. (3, 5)
d. (3, 1)

1. what is the equation of the line?

a. y = 2
b. x = -2
c. y = -2
d. x = 2

Explanation:

Step1: Rewrite the equation in slope - intercept form for question 1

The slope - intercept form is $y = mx + b$. Starting with $4y-2x=-20$, first add $2x$ to both sides: $4y=2x - 20$. Then divide each term by 4: $y=\frac{2}{4}x-\frac{20}{4}=\frac{1}{2}x - 5$. There seems to be a mistake in the problem setup as none of the given options are correct. But if we assume it was supposed to be $4y+2x=-20$, then $4y=-2x - 20$ and $y =-\frac{1}{2}x-5$. If we assume it was $2y - x=- 10$ (a possible mis - writing), then $2y=x - 10$ and $y=\frac{1}{2}x - 5$. Let's assume the correct equation is $4y-2x=-20$ and re - check our work. Add $2x$ to both sides: $4y=2x - 20$, then $y=\frac{1}{2}x - 5$.

Step2: Find the coordinates of point B for question 2

The mid - point formula is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A(x_1,y_1)=(-13,9)$ and $M(x_m,y_m)=(-2,5)$. For the x - coordinate: $\frac{-13 + x_2}{2}=-2$. Multiply both sides by 2: $-13+x_2=-4$. Then add 13 to both sides: $x_2 = 9$. For the y - coordinate: $\frac{9 + y_2}{2}=5$. Multiply both sides by 2: $9 + y_2 = 10$. Subtract 9 from both sides: $y_2=1$. So $B=(9,1)$.

Step3: Find the coordinates of point P for question 3

The section formula for a point $P(x,y)$ that divides the line segment joining $X(x_1,y_1)$ and $Y(x_2,y_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here $x_1=-1,y_1 = 2,x_2 = 7,y_2 = 14,m = 1,n = 3$. Then $x=\frac{1\times7+3\times(-1)}{1 + 3}=\frac{7 - 3}{4}=1$ and $y=\frac{1\times14+3\times2}{1 + 3}=\frac{14 + 6}{4}=5$. So $P=(1,5)$.

Step4: Determine the equation of the line for question 4

The line is a horizontal line. For a horizontal line, the equation is of the form $y = k$, where $k$ is a constant. The line passes through the point where $y=-2$. So the equation of the line is $y=-2$.

Answer:

1. None of the above
2. C. $(9,1)$
3. A. $(1,5)$
4. C. $y=-2$