Algebra 2 question

Question

Which of the following is a correct equation for the line passing through the point (-2,1) and having slope m=1/2 

 

Check all that apply

 

A. y=1/2x + 2

 

B.y=-2x + 1/2 

 

C. x-2y= -4

 

D. y-1= 1/2(x+2)

Answer 1

A    is yes    (This equation is presented in slope-intercept form. The slope is 1/2 while the y-intercept is 2 or (0,2)).

 

B    is  no     (The slope here is -2 , not 1/2) The point (-2,1) will satisfy both this equation and the original. The product of their slopes is -1. This tells us that these linear equations intersect at a right angle. One could state that they are perpendicular equations and the two slopes are negative reciprocals of each other. The point of intersection is (-2,1) since that point "satisfies" both of these equations. Please recall that if two straight lines intersect they do so in only one point.)

 

C    is yes    (Its the same equation as the first one, just presented here in Standard Form.)

 

D    is yes    (Its the same equation as the first one, but presented here in point-slope form.)

Answer 2

The first step to solving this problem is to rewrite any equation in the y = mx + b format that isn't already there.

a) fine as is
b) fine as is
c) solving for y gets us:
x-2y=-4
2y = x + 4
y = 1/2x + 2 ((the same as answer a))
d) solving for y gets us:
y-1=1/2(x+2)
y-1=1/2x + 1
y = 1/2x + 2 ((the same as answers a and c))

 

At this point, if you were unsure, three answers being the same should be a hint. But continuing onwards.

 

In the y=mx+b format, m is slope and b is the y intercept. So we can eliminate answer b since the slope does not equal 1/2.

 

To confirm that the point (-2,1) is on the remaining function, y=1/2x + 2, we simply plug into the problem.

 

(1) = 1/2 (-2) + 2

1 = -1 + 2

1 = 1.

 

Therefore the point is on the line and the line has the slope needed. Answers a, c, and d are all correct.

Answer 3

Aaliyah,

 

Recall the formula for finding the equation of a line is that given a point P(x₁,y₁) the equation of the line is

 

(y - y₁) = m·(x - x₁) where m is the slope and x₁ and y₁ are the coordinates of the given point , so you have:

 

m = ½, x₁ = -2, and y₁ = 1

 

Plugging in these numbers:  (y - 1) = ½·(x - (-2)) = ½·(x + 2)

 

So (y - 1) = ½·(x + 2) looks just like answer D, but we can simplify further to get:

 

y = ½·x + 1 + 1 = ½·x + 2 which is answer A.  So both A & D are correct.

 

Answer B is clearly wrong, since in its simplified form slope = -2 and b = 1/2 clearly don't match with A0.

 

What about answer C?  If you rearrange:  x = 2·y - 4 ⇒ ½·x = y - 2 ⇒ ½·x + 2 = y which is also = A)

 

So C is also a solution.