Find the equation of the line in slope-intercept

Ответ:

jpsaad00

16.03.2022

Mathematics

An equation in slope-intercept form of the line will be

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

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where m is the slope and b is the y-intercept

Given the points

(-1, -1) (1, 0)

Finding the slope between (-1,-1) and (1,0)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-1,\:-1\right),\:\left(x_2,\:y_2\right)=\left(1,\:0\right)$

$m=\frac{0-\left(-1\right)}{1-\left(-1\right)}$

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

substituting m = 1/2 and (-1, -1) in the slope-intercept form of the line equation to determine the y-intercept

y = mx+b

$-1=\frac{1}{2}\left(-1\right)+b$

$-\frac{1}{2}+b=-1$

Add 1/2 to both sides

$-\frac{1}{2}+b+\frac{1}{2}=-1+\frac{1}{2}$

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

substituting m = 1/2 and b = -1/2 in the slope-intercept form of the line equation

y = mx+b

$y\:=\frac{1}{2}x+\left(-\frac{1}{2}\right)$

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

Therefore, an equation in slope-intercept form of the line will be

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

0,0(0 оценок)

Ответ:

treaustin656

17.01.2023

Mathematics

The path of the fireworks is the path of a projectile and are therefore

parabolic.

The correct responses are;

1.) The equation in general form is; f(x) = 10·x - 0.5·x²

2.) Equation of the path of firework #2 is; f(x) = -0.5·(x - 10)² + 72

3.) The domain of firework #1 is; 0 ≤ x ≤ 20

The range of firework #1 is; 0 ≤ f(x) ≤ 50

Reasons:

1.) The given parameters for the firework #1 are;

Coordinates of the vertex = (10, 50)

Shape of the path = Parabolic

Required:

Equation for the path of firework #1.

Solution:

The vertex form of a quadratic equation is presented as follows;

f(x) = a·(x - h)² + k

Where;

The vertex = (h, k)

Therefore, when f(20) = 0, we get;

f(20) = 0 = a·(20 - 10)² + 50 = 100·a + 50

$a = -\dfrac{50}{100} = -\dfrac{1}{2}$

Which gives;

$f(x) = -\dfrac{1}{2} \cdot (x - 10)^2 + 50 = -\dfrac{1}{2} \cdot x^2 +10 \cdot x = 10\cdot x - 0.5 \cdot x^2$

Height = f(x) = 10·x - 0.5·x²

2.) The equation of the second firework is given as follows;

The vertex of the firework = (10, 72)

f(x) = a·(x - h)² + k

Therefore;

f(x) = a·(x - 10)² + 72

when f(22) = 0, we get;

f(22) = 0 = a·(22 - 10)² + 72 = 144·a + 72

$a = -\dfrac{72}{144} = -\dfrac{1}{2}$

The equation of the path of the firework in vertex form is therefore;

$f(x) = -\dfrac{1}{2} \cdot (x - 10)^2 + 72$

f(x) = -0.5·(x - 10)² + 72.

3.) The domain and range of firework one #1 is given as follows;

The domain = 0 ≤ x ≤ 20

The range of firework #1 is therefore;

0 ≤ f(x) ≤ 50

Learn more here:

0,0(0 оценок)

Find the equation of the line in slope-intercept form (-1,-1) and (1,0)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question