All categories

2 years ago

Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?

Mathematics

1 answer:

frosja888 [35]2 years ago

6 0

Answer:

7x + 2y = 1

Step-by-step explanation:

1. Find the slope of the line.

(y2-y1)/(x2-x1) ----> (11 - (-3))/((-3) -1) ----> (11+3)/ (-3 -1) ----> 14/-4

*lets simplify into (7/-2)*

2. Write into slope intercept form.

y=mx+b (m is the slope) (b is the y intercept)

y = (7/-2)x + b

We now need to find the value of b, this can be done by plugging in values of x and y, and using algebra to solve.

11 = (7/-2)(-3) + b

11 = 10.5 + b

b = 0.5 or 1/2

slope intercept form y = (7/-2)x + 1/2

Now we convert to standard form: ax+by=c

*In this form we our a term cannot be a fraction nor can it be negative*

1. Get x and y on the same side, and since our x term is negative right now, we can make it positive by adding it on both sides.

(7/2)x + y = 1/2

2. We now want to get rid of the fraction in term a, so we multiply the entire function by two, so the denominator cancels out.

2(7/2)x + 2y = 2(1/2)

Simplify and you get

7x + 2y = 1

You might be interested in

What is the length of the longest possible laser beam he could send rounded to the nearest tenth of an inch?

Ludmilka [50]

Where is the diagram????????

3 0

3 years ago

Plzzz help me with this I’ll give brainliest

scoray [572]

Answer18:

The quadrilateral ABCD is not a parallelogram

Answer19:

The quadrilateral ABCD is a parallelogram

Step-by-step explanation:

For question 18:

Given that vertices of a quadrilateral are A(-4,-1), B(-4,6), C(2,6) and D(2,-4)

The slope of a line is given m= $\frac{Y2-Y1}{X2-X1}$

Now,

The slope of a line AB:

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{6-(-1)}{(-4)-(-4)}$

m= $\frac{7}{0}$

The slope is 90 degree

The slope of a line BC:

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{6-6}{(-4)-(-1)}$

m= $\frac{0}{(-3)}$

The slope is zero degree

The slope of a line CD:

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{(-4)-6}{2-2}$

m= $\frac{-10}{0}$

The slope is 90 degree

The slope of a line DA:

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{(-1)-(-4)}{(-4)-(2)}$

m= $\frac{3}{-6}$

m= $\frac{-1}{2}$

The slope of the only line AB and CD are the same.

Thus, The quadrilateral ABCD is not a parallelogram

For question 19:

Given that vertices of a quadrilateral are A(-2,3), B(3,2), C(2,-1) and D(-3,0)

The slope of a line is given m= $\frac{Y2-Y1}{X2-X1}$

Now,

The slope of a line AB:

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{2-3}{3-(-2)}$

m= $\frac{-1}{5}$

The slope of a line BC:

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{(-1)-2}{2-3}$

m= $\frac{-3}{-1}$

m=3

The slope of a line CD:

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{0-(-1)}{(-3)-2}$

m= $\frac{-1}{5}$

The slope of a line DA:

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{3-0}{(-2)-(-3)}$

m=3

The slope of the line AB and CD are the same

The slope of the line BC and DA are the same

Thus, The quadrilateral ABCD is a parallelogram

3 0

3 years ago

Bob believes his test grade varies directly with the number of hours he spends studying and inversely with the number of hours h

Readme [11.4K]

Answer: Hello mate!

A direct variation implies that, if y is the dependent variable that varies with the variable x; then: y = k*x where k is a real number.

An inverse variation has the form y = k/x where also k is a real number.

them, if we define s as the hours that Bob spends studying, and b as the hours that he spends playing baseball, then the equation that represents the score is:

Score(s,b) = k*s/b

we know that if s = 6, and b = 7, then the score is 72; with this information, we could obtain the value of the constant k.

score(6,7) = 72 =k*6/7 = k*

then k = 72*(7/6) = 61.7

now if s = 4 and b = 6, the score that he should expect is:

score( 4, 6) = 61.7*(4/6) = 41

6 0

3 years ago

Please help asap. thanks

sergeinik [125]

Answer:

4 $\sqrt{2}$

Step-by-step explanation:

use pythagoeron theorem

9^2-7^2=x^2

x^2=32

x=4 $\sqrt{2}$

4 0

3 years ago

Read 2 more answers

The family wants to determine if they can drive to the national park using Just one tank of gas in their car. Determine whether

Nataliya [291]

Answer:

The Fullers can reach the national park

Step-by-step explanation:

<u><em>The complete question is</em></u>

The Fuller family wants to drive to a national park. Some information about their trip is given in the table below.

Distance to national park 515 miles

Car’s gas tank capacity 20 gallons

Average gas mileage for car 26 miles per gallon

The family wants to determine if they can drive to the national park using just one tank of gas in their car. Determine whether the Fullers can reach the national park. Show your work or explain your answer.

we know that

The Average gas mileage for the car is 26 miles per gallon

That means

With 1 gallon the car runs 26 miles

using a proportion

Find out how many miles the car runs with 20 gallons (one tank of gas)

$\frac{26}{1}\ \frac{miles}{gallon}=\frac{x}{20}\ \frac{miles}{gallons}\\\\x=26(20)\\\\x=520\ miles$

Compare with the distance to the national park

$520\ miles>515\ miles$

therefore

The Fullers can reach the national park

7 0

3 years ago