Which one of these equations passes through points (1,3) and (-2,-3)?

Question

Possible Equations:
B) y=x+1
D) y=2x+1
F) y= 2/3x +1

#30)An equation that passes through (2,2) and (-3,-1).
#32) Anequation that passes through (1,2) and (-2,-1).

Answer 1

Substitute x and y into the equations to determine which equations pass through the points.

Use these points first: 1,3
3 = 1 + 1 is false. B is out.
3 = 2 + 1 is true.
3 = 2/3 + 1 is false. F is out.

D is the only equations that has the point (1,3).

Now substitute -2,-3 into D to check if it satisfies the other point.

-3 = -4 + 1 is true. D passes through both points.

Answer 2

D). y = 2x + 1

3 = 2(1) + 1
&
-3 = 2(-2) +1

#30) the general equation for a line is y = mx + c
First find 'm' the slope
m = (-1-2) /( -3 -2)
m = -3 / -5
m = 3/5

Next find 'c' the y- intercept.
y = 3x/5 + c Taking either point and substituting in #
2 = 2(2)/5 + c
2 = 4/5 + c
c = 2 - 4/5 = 1 1/5 = 6/5
Eq'n is y = 3x/5 + 6/5
which rearranged gives 5y - 3x = 6

#32)the general equation for a line is y = mx + c
First find 'm' the slope
m = (-1-2) /( -2 -1)
m = -3 / -3
m = 3/3 = 1 NB the coefficient of '1' is not indicated before any algebraic letter. The letter, 'x' in this case, stands alone.

Next find 'c' the y- intercept.
y = x + c Taking either point and substituting in
2 = 1 + c
c = 2 - 1 = 1
Eq'n is y = x + 1
which rearranged gives y - x = 1

Answer 3

Simply choose one of the points in the problem and plug the x in for x and the y in for y in each equation and see what works.

I chose point (-3,-1)

equation F) y= 2/3x+1
-1= (2/3)(-3)+1
-1= -2+1
-1 = -1
so #30 is equation F

Choose point (-2,-1)

Equation B) y = x + 1
-1 = -2 + 1
-1 = -1
So # 32 equals out to be equation B

Answer 4

find the slope(m) : (y2 - y1) / (x2 - x1)
(-3 - 3) / (-2 - 1) = (-3 + -3) / (-2 + -1) = -6 / -3 = 2

then use formula y - y1 = m(x -x1)
y - 3 = 2(x - 1)

finally switch it around so that it is y = mx + b
y -3 = 2x - 2
y = 2x + 1

answer is D

#30)
(-1 - 2) / (-3 - 2) = (-1 + -2) / (-3 + -2) = -3 / -5 = 3/5

y - 2 = 3/5(x - 2) i usually leave it like this

hope you can do the last one on your own

Answer 5

Just calculate the slope = (change in y)/(change in x) = 2. So D is the only possible answer.

For the others set up y = mx + b, calculate the slope from the points given, and the solve for b given x,y, and m.