3. The temperature of a swimming pool

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept
Parallel lines always have the same slope (m)

Determine the slope (m):

$y=\displaystyle-\frac{4}{3}x -1$

The slope of the given line is $\displaystyle-\frac{4}{3}$ , since it is in the place of m in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be $\displaystyle-\frac{4}{3}$ . Plug this into y=mx+b:

$y=\displaystyle-\frac{4}{3}x+b$

Determine the y-intercept (b):

$y=\displaystyle-\frac{4}{3}x+b$

To find the y-intercept, plug in the given point (6,14) and solve for b:

$14=\displaystyle-\frac{4}{3}(6)+b\\\\14=-8+b\\b=22$

Therefore, the y-intercept of the line is 22. Plug this back into $y=\displaystyle-\frac{4}{3}x+b$ :

$y=\displaystyle-\frac{4}{3}x+22$

I hope this helps!

5 0

2 years ago

Find the largest of 3 consecutive odd integers that have a sum of -75

Vika [28.1K]

Odd integers are 2 apart

they are
x,x+2,x+4

sum is -75

x+x+2+x+4=-75
3x+6=-75
minus 6 both sides
3x=-81
divide both sides by 3
x=-27
x+2=-25
x+4=-23

the largest is the farthest to right on a number line
largest is -23

3 0

2 years ago

A die is rolled. Find the probability of the given event. (a) The number showing is a 2; The probability is : (b) The number sho

Sphinxa [80]

Answer:

(a) 1/6

(b) 1/2

(c) 1/3

Step-by-step explanation:

There are 6 possible outcomes.

(a) The number is 2: only 1 outcome out of 6, hence 1/6

(b) The number is even: {2, 4, 6} - 3 outcomes out of 6, hence 3/6 = 1/2

(c) The number is greater than four: {5, 6} - 2 outcomes out of 6, hence 2/6 = 1/3

5 0

1 year ago