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2 years ago

Graph the line that passes through the points (-5, 3) and (−1,−1) and determine the equation of the line.

Mathematics

1 answer:

Charra [1.4K]2 years ago

4 0

A line can be drawn by joining the plot of the two given points

Please find attached the graph of the line created with MS Excel

The equation of the line is y = -x - 2

Reason:

Given points on the line are (-5, 3) and (-1, -1)

From the given points, the graph of the line can be plotted with MS Excel

The slope, m, of the line is given as follows

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Therefore, we have;

$Slope, \, m =\dfrac{-1 - 3}{-1 - (-5)} = \dfrac{-4}{4} = -1$

The equation of the line in point and slope form is therefore;

y - 3 = -1·(x - (-5) = -x - 5

In slope and intercept form, we have;

y = -x - 5 + 3 = -x - 2

The equation of the line in slope and intercept form is y = -x - 2

Learn more here:

brainly.com/question/2088114

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Answer:

9.5

Step-by-step explanation:

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2 years ago

If line d intersects plane f, then how many points on line d also lie on plane f?

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3 years ago

Read 2 more answers

F(x) = x^2. What is g(x)

Alexeev081 [22]

Answer:

g(x) = - x² - 4 ⇒ A

Step-by-step explanation:

Let us revise the reflection and translation of a function

If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)

If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)

If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k

If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k

f(x) = x² is the blue curve

g(x) is its image is the red curve

∵ g(x) is the image of f(x)

∵ f(x) is opened upward

∵ g(x) is opened downward

→ That means the sign of y-coordinates of all points on the blue

graph are opposite

∴ f(x) is reflected about the x-axis

∴ Its image is - f(x)

∵ The vertex of f(x) is (0, 0)

∵ The vertex of g(x) = (0, -4)

→ That means the function translated 4 units down

∴ - f(x) is translated 4 units down

∴ Its image is - f(x) - 4

∴ g(x) = - f(x) - 4

∵ f(x) = x²

∴ g(x) = - x² - 4

4 0

3 years ago

A cookie factory uses 7/10 of a barrel of oatmeal in each batch of cookies. The factory used 4 9/10 barrels of oatmeal yesterday

melamori03 [73]

Answer: 7 BATCHES

Step-by-step explanation: to produce one batch it takes 7/10 of oatmeal

Now the factory uses 4 9/10 batch of oatmeal

1=7/10 OATMEAL

X=4 9/10 OATMEAL

X=(7/10*1)/4 9/10

=4 9/10*10/7

=490/70

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2 years ago

Two cars start from the same point driving in opposite directions. Both cars drive 6miles. One car stops, the other car makes a

dimaraw [331]

Answer:

14.4 mile²

Explanation:

1. By driving 6 miles each, the cars will be 6 miles + 6 miles = 12 miles appart.

2. When one car stops and the other car makes a 90° left-hand turn and drive 8 miles, you can model the situation with a right triangle, where one leg is 12 miles, the other leg is 8 miles, and the hypotenuse is the distance that separates the cars.

Hence, you must use Pythagoras to find that distance.

3. Pythagoras

hypotenuse² = leg₁² + leg₂²

hypotenuse = (12 mile)² + (8 mile)² = 144 mile² + 64 mile² = 208 mile²

$hypotenuse=\sqrt{208mile^2}=14.4mile^2$ , which is rounded to the neartest tenth of a mile.

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3 years ago