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3 years ago

Write the slope-intercept form of the equation of the line through the given points. (0,3) and (-4 -1)

Mathematics

1 answer:

Scilla [17]3 years ago

7 0

Answer:

Step-by-step explanation:

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-4, -1) and (0, 3) → b = 3.

Calculate the slope:

$m=\dfrac{3-(-1)}{0-(-4)}=\dfrac{4}{4}=1$

Therefore we have the equation:

y = 1x + 3

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How many real-number solutions does the equation have?

Nataly_w [17]

Answer:

Option b. Two solutions

Step-by-step explanation:

In order to find how many real number solutions the equation has we have to solve it

Given equation: -4x² + 10x + 6 = 0

taking 2 common from the equation

2(-2x² + 5x + 3) = 0

-2x² + 5x + 3 = 0

taking minus sign common from the above equation

2x² - 5x - 3 = 0

We will solve this equation by factorization in such a way that the sum of two factors is equal to -5x and the product is -6x²

2x² - 6x + x - 3 = 0

taking common above

2x(x-3) + 1(x-3) = 0

taking (x-3) common

(2x+1)(x-3) = 0

2x + 1 = 0

2x = -1

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

x - 3 = 0; x = 3

the solutions are

$x=\frac{-1}{2},3$

Both values are real numbers, therefore correct option is b

7 0

3 years ago

Read 2 more answers

Let a, b, c, and d be real numbers with a, c 6= 0. Prove that the lines y = ax+b and y = cx + d have the same x-intercept if and

Monica [59]

Step-by-step explanation:

We have got the lines :

$y=ax+b\\y=cx+d$

Both lines intercept the x-axis in the point :

$I = (i_{1} ,i_{2})$

In all point from x-axis the y-component is equal to 0.

$I=(i_{1},o)$

We replace the I point in the lines equations:

$0=a(i_{1})+b \\0=c(i_{1})+d$

From the first equation :

$0=a(i_{1})+b \\-b=a(i_{1})\\i_{1}=\frac{-b}{a}$

From the second equation :

$0=c(i_{1})+d\\ -d=c(i_{1})\\i_{1}=\frac{-d}{c}$

Then $i_{1}=i_{1}$

Finally :

$\frac{-b}{a}=\frac{-d}{c} \\\frac{b}{a}=\frac{d}{c} \\ad=bc$

y = ax + b and y = cx + d have the same x-intercept ⇔ad=bc

8 0

3 years ago

Angles BAE and FAC are straight angles. What angle relationship best describes angles BAC and EAF?

Vika [28.1K]

The best angle relationship that describes angles BAC and EAF is supplementary angles

The sum of angle on a straight line is supplementary i.e. they sum up to 180 degrees.

If Angles BAE and FAC are straight angles, it means they are linear pairs and their sum is 180 degrees. Mathematically;

m<BAE + m<FAC = 180degrees

Hence we can conclude that the best angle relationship that describes angles BAC and EAF is supplementary angles

Learn more here: brainly.com/question/22309882

7 0

3 years ago

If J/24 = K, then J/6 =

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

$\frac{J}{24}$ = K ( multiply both sides by 24 to clear the fraction )

J = 24K ( divide both sides by 6 )

$\frac{J}{6}$ = 4K

8 0

3 years ago

1.) Divide $80 among three people so that the second will have twice as much as the first, and the third will have $5 less than

Marina CMI [18]

1 ) The first person will have $17. The second person will have $34 and the third person will $29.

5 0

3 years ago