A Triangle's Area
Each of two congruent triangles has an area of 24 square units. Their vertices are determined by the intersection of the lines with equations:
y = -4
x = 0
y = (-3/4)x + b
Determine the two values of b that will identify the lines needed to form these triangles.
You may want to use some graph paper as you investigate and analyze this problem; however, a drawing is not required in your submission.
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ReplyDeleteS.R.
ReplyDeleteb=-4,0
i got the answer by solving for the equation for b.
because 3/4 time 0 is 0 so -4=b b had to be -4
M.N.H. B=-4,0
ReplyDeleteI got this answer by solving the equation for the variable B. Because 3/4 x 0 is 0, so -4=b and had to be -4.
MS. -4=b
ReplyDeleteA.C.M.
ReplyDelete-4=b I got this by solving for b. After plugging in y and x, the equation was -4=(-3/4)0+b.
Since -3/4 times 0 is 0, I knew that -4 had to equal b.
J.H.
ReplyDeleteAll of the triangles have an area of 24 square units. For both of the one of the triangles, would have to be. The equation for one of the triangles would be y=(-3/4)24+42. Another equation could be -4=3/4(0)+28. Then b would equal -4.
MJH
ReplyDeleteB=-4
Y= (-3/4) X+B
-4= (-3/4) 0+B
0 times -3/4 is 0, so 0 + -4 equals -4.
S.G.
ReplyDelete-4=B
-4 must equal B because if y is -4, and x is 0, then the equation y= (3/4) x + B really is -4= (3/4) (0) + B. Which equals -4= B.
A.A.M.
ReplyDeleteWhen solving the equation -3/4 multiplied by 0 would be 0 leaving -4 to equal b.
-4=-3/4(0)+b
-4=b
JR B=-4,0
ReplyDeleteI got the awnser by solving for B. Since it is 3/4x I replaced x with zero which made it zero. Then y is -4=b so b=-4.
E.D.
ReplyDelete-4=b
The equation is y=mx+b.
They give us x= 0 and y= -4
Plug them into the equation, making it -4=m0+b.
The slope they gave us was -3/4.
That being m, now the equation is -4=(-3/4)0+b.
We are looking for b, so we need to solve the equation.
-4=(-3/4)0+b
-4=0+b
-4=b
O.S
ReplyDeleteb=-4
Since y = -4, -3/4 must go away. Luckily, the format is y=mx+b, and x=0.
-3/4x0=0
0+-4=-4
B.H.
ReplyDeleteThe equation was: y=(-3/4)x+b. It gave you x and y to fill into the equation (0,-4). If you plug these numbers into the equation, the equation is -4=(-3/4)0+b. 0 times -3/4 equals 0. So the remaining of the equation is -4=b. The y-intercept is equal to -4.
If you solve for the x-intercept and you plug in (-4, 0), the equation is 0=(-3/4)4+b. -4 times -3/4 equals 3. Now you have 0=3+b. Subtract 3 from both sides and you get -3=b. The x-intercept is equal to -3.
M.N
ReplyDeleteI got the answer by substituting y for -4. So the equation would look like -4=-3/4x + b. We already know that x = 0 so immediately you get the answer -4=b. So it would be (0,-4)
M.D.
ReplyDeleteA Triangle's Area
Each of two congruent triangles has an area of 24 square units. Their vertices are determined by the intersection of the lines with equations:
y = -4
x = 0
y = (-3/4)x + b
Determine the two values of b that will identify the lines needed to form these triangles.
You may want to use some graph paper as you investigate and analyze this problem; however, a drawing is not required in your submission.
First, I plugged in the y and x values so that I could solve for b.
-4= -3/4(0)+b
I found out that b equals negative four.
Then I started plotting the points to figure out the location of the triangle. I started at (0,0) and then plotted (0,-4), then plugged in the equation to find the next point, which was
(-4,-1). To get the next triangle, I just reflected the triangle over the x-axis. My new points were (0,0), (-4,3), and (0,4). Once I got the triangle, I knew I still needed to solve for the new b, so I worked backwards using the points (-4,3).
3=(-3,4)-4+b. After solving the equation, I found that b=0.
M.W.
ReplyDeleteSubstitution and solving for b
-4= (-3/4)0 +b
-4=0+b
-4=b
-4 = (-3/4)0+-4
y = (-3/4)x +-4
x (-4,0)
y (0,0)
I graphed the equation y = (-3/4)x+-4 and got the coordinate point, (-4, -1). Then I got the coordinate points of the x and y that was given to me. They were, x = (-4, 0) and y = (0,0). Graphing those three points gave me a triangle. In order to create that same triangle with a different value of b, I shifted the triangle on my graph four units up in the graph. So the new coordinate points would be x= (0,0) y= (0,4), and the equation point would be (-4, 3). So it is the same triangle, same area, but the coordinate points are different. I tried to create the equation again with the new triangle that I made, and I got y=-3/4x +0. I found the slope between the coordinate point, (-4,3) and (0,0) and got ¾. Then the y-intercept would be 0 because that is where it crosses the y axis, at 0. So the new equation would be y=-3/4x +0. The two values of b are -4 and 0.
P.M.
ReplyDeleteif you plug in the values into the equation, you can figure out that b is -4.
Here is how:
Y=mx+b
Plug in the values, and it becomes…
-4=-3/4(0) + b
-4 = 0+ b
JL
ReplyDeleteA Triangle's Area
Each of two congruent triangles has an area of 24 square units. Their vertices are determined by the intersection of the lines with equations:
y = -4
x = 0
y= (-3/4)x + b
Determine the two values of b that will identify the lines needed to form these triangles.
You may want to use some graph paper as you investigate and analyze this problem; however, a drawing is not required in your submission.
The first thing you need to do is plug in the values of Y, -4, and X, 0, in the slope intercept form equation, -4= (-3/4)0+b.
-4=0+b
-4=b
-4= (-3/4)0+ (-4)
b=-4 is the first value. Then I plotted the points, -4,-1, 0,0, and 0,-4. Then I just reflected the triangle over the X-axis and found the new coordinates for the new slope intercept equation for the new value of b.
y= mx+b
y= (3/4)x+b
4= (3/4)0+b
4=0+b
4=b
N.H.
ReplyDeleteBy plugging in the values of 0 into the equation you will find that the first value b is -4. This is because (-3/4)0= -4. So -4 =b. The second is y=7, which closes the triangle.
P.M.
ReplyDeleteRevision over last comment:
if you plug in the values into the equation, you can figure out that b is -4.
Here is how:
Y=mx+b
Plug in the values, and it becomes…
-4=-3/4(0) + b
-4 = 0+ b
If you use 7, it closes down the triangle, which I found by testing it in a graph.
C.A.
ReplyDeleteIf you plug in x(0) and y(-4) into the equation, you get -4=-3/4(0)+b. You automatically know that -4=b because -3/4 times 0 is 0 and 0+b is equal to b.
J.H.S
ReplyDeleteOctober 15th POW
I Solved the equation: -4= (-3/4)(0)+b to get the answer. This is how I approached the problem:
-4= (-3/4)(0)+b
-4=0+b
-4=b
S.S.
ReplyDelete-4,0 = b
The way I got the answer was I started out by solving the equation for the variable B. When plugging in the number the equation is -4=(-3/4)0+b. Part of the equation, as you see, is -3/4 times zero and anything times zero is zero, which means Y is equivalent to B.