1. What is the slope of 3x-4y=6 ?
Let’s put it in the slope-intercept form (y=mx+b). That means we need to get y all by itself on the left side of the equation.
Let’s put it in the slope-intercept form (y=mx+b). That means we need to get y all by itself on the left side of the equation.
Take away 3x from both sides: -4y = -3x + 6
Now divide everything by -4: y = ¾ x - 6/4 or y = ¾ x – 3/2.
So the slope is ¾
.
2. What point is not on
the line that the others are on?
(2,5), (3,8),
(4,11), (6,17), (8,20)
There are several ways we can solve this.
If you like to draw graphs, do that.
If you understand “slope = rise over the
run” that would be easy.
Or if you like charts and patterns we could
do that.
Lets do “rise over run.” Rise is how far
up, run is how far to the right to the next point.
From (2,5) to (3,8) Rise is 8-5=3. Run is
3-2=1. Slope = 3/1.
From (3,8) to (4,11) Rise is 11-8=3. Run is
4-3=1. Slope = 3/1.
From (4,11) to (6,17) Rise is 17-11=6. Run
is 6-4=2. Slope = 6/2 = 3/1.
From (6,17) to (8,20) Rise is 20-17=3. Run
is 8-6=2. Slope = 3/2. Aha!! (8,20) is not on
the same line!
33. What is the equation of
the line parallel to y = ¾ x – 2 that passes through the point (8,1)?
Parallel lines have the same slope, so our
equation will be y = ¾ x + b. All we
have to do is figure out b and we
have an equation. But it passes through (8,1) which means our equation is true
when x=8 and y=1.
So 1 = ¾ (8) + b.
Or 1 = 6 + b. therefore b must be -5. So the equation we were
looking for is:
y = ¾ x – 5.
Let’s re-read the question. Is our
equation’s line parallel to the given line? You bet – they both have a slope of
¾ . Does it pass through (8,1). Let’s double-check. 1 = ¾ (8) – 5. ¾ of 8 is 6
so does 1=6-5? Yes!
44. What is the equation of thee line perpendicular to y = ¾ x – 2 that passes through the point (9,1)?
This is similar to the previous problem but this time the line is perpendicular instead of parallel. To find the slope of the perpendicular, you take the negative reciprocal. So the slope of our line will be -4/3. The equation will be y = -4/3 x + b. We know when x=9, y=1 so to figure out b, we plug those values into our equation:
This is similar to the previous problem but this time the line is perpendicular instead of parallel. To find the slope of the perpendicular, you take the negative reciprocal. So the slope of our line will be -4/3. The equation will be y = -4/3 x + b. We know when x=9, y=1 so to figure out b, we plug those values into our equation:
1 = -4/3 (9) + b
1 = -12 + b
13 = b
so our equation is y = -4/3 x + 13
5.5. Olivia sees a
model of a pyramid that has a square base. The base of the pyramid was 6 inches
long and the area of each one of the four sides was 12 sq. in. She would like
to make her model larger. Her base will be a foot long.
a) If she builds
it proportionally, what will be the total area of the 4 sides of her completed
pyramid?
Doubling the length will quadruple the
area. The area of a side was 12 sq.in. The new area of a side will be 4x12=48.
The area of all 4 sides will be 4x48=192 sq. in.
b) How long is
each of the 4 edges leading to the top of her pyramid?
Her pyramid has a base of 12” and area of
48 sq. in. Since the formula for the area of a triangle is A = ½ bh,
48 = ½ (12) h
48 = 6 h
8 = height By
dividing the triangle in two from top to bottom, we get a right triangle with
base 6 and height 8. What is the edge? Use the Pythagorean theorem a2+b2=c2:
62 + 82 = h2. Hence 36+64 = h2 or 100 = h2
and h the hypotenuse, which is the edge of the pyramid, = 10 in.
The only one above zero today was Sophia with 2 points.
These problems required algebra.
| Oscar Halverson | 50.0 |
| Cyrus Martin Ri | 36.0 |
| Nick Wendt | 30.0 |
| Sophia Schomer | 25.0 |
| Nina Kessler | 18.0 |
| Miles Dunn | 17.0 |
| Dain Dolan | 15.0 |
| Will Gannon | 15.0 |
| Duy Houng | 13.0 |
| Amario Sisakda | 12.0 |
| Lucas Lindgren | 11.0 |
| Lily Pince | 11.0 |
| Ellyanna Lee | 10.0 |
| Charles Cheesebrough | 10.0 |
| Melissa Irwin | 8.0 |
| Claire Newmark | 7.0 |
| Jackson Cercioglu | 6.0 |
| Stella Warwick | 6.0 |
| Victoria Dzurilla | 2.0 |
HERITAGE
The only ones above zero today were Anthony with 12 and Ben with 2.
| Anthony Rocke | 69.0 |
| Kathryn Lewis | 31.0 |
| Ben Nickson | 30.0 |
| Steve Nickson | 24.0 |
| Aidan Mallberg | 13.0 |
| Emma Lawrence | 13.0 |
| Colten Bartlette | 5.0 |
| Dia Balderramos | 6.0 |
| Maraya Lucio | 4.0 |
| Alycia Gonzales Lewis | 4.0 |
| Ruby Lipschultz | 6.0 |
| Sophie Todaro | 2.0 |
