All categories

3 years ago

What is the equation of the line that goes through the point (0,2) and has a slope of -1

Mathematics

1 answer:

givi [52]3 years ago

8 0

Answer:

y = -x + 2

Step-by-step explanation:

The point (0,2) is the y-intercept.

The equation of a line is y=mx + b.

The b variable represents the y-intercept.

The m variable represents the slope.

Substitute -1 for the slope and 2 for the y-intercept into the equation.

y = mx + b

y = (-1)x + (2)

y = -x + 2

You might be interested in

What is the solution to y = x + 2 and y = 3x – 2 and how do you know? PLEASE HELPPPPP! THANK U!

Nutka1998 [239]

Answer:

(2,4)

Step-by-step explanation:

We have the system:

y=x+2

y=3x-2.

This is already setup for substitution.

I'm going to replace my first y with what the second y equals.

That is, I'm going to write 3x-2=x+2.

Time to solve the following for x:

3x-2=x+2

Subtract x on both sides:

2x-2= 2

Add 2 on both sides:

2x. = 4

Divide both sides by 2:

x. = 2

Now that we know x=2 and we have an equation that relates x to y: either y=x+2 or y=3x-2, doesn't matter which we use, we can find y.

So we y=x+2 with x=2 which means y=2+2=4.

So the solution, the intersection, is (2,4).

5 0

3 years ago

Read 2 more answers

Help it’s slope idk how to do it

Over [174]

a. $\boxed{y-602=\frac{2}{3}(x-3)}$

b. For every month the pine tree grows about 0.67 inches.

c. <em> </em>It represents the height of the tree at the moment Ariel started to record the heights.

<h2>Explanation:</h2>

In this exercise we have that in July Ariel recorded the height of a pine tree and how quickly it was expected to grow in next several months. From the Table, we can get the following points:

$P_{1}(3,602) \\ \\ P_{2}(6,604) \\ \\ P_{3}(q,606) \\ \\ P_{4}(12,608)$

It is obvious that this problem follows a linear equation, so our goal is to find the equation that matches the Table.

The point slope form of the equation of a line is:

$y-y_{1}=m(x-x_{1}) \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{1}, y_{1}):A \ point \ on \ the \ line$

Finding (m):

$Using: \\ \\ P_{1}(x_{1},y_{1}) \rightarrow P_{1}(3,602) \\ \\ P_{2}(x_{2}, y_{2}) \rightarrow P_{2}(6,604) \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{604-602}{6-3} \\ \\ m=\frac{2}{3}$

Finally, the equation of the line is:

$(x_{1}, y_{1}) \rightarrow (3,602) \\ \\ \boxed{y-602=\frac{2}{3}(x-3)}$

In this case, we have that:

The x-axis represents the <em>Number of Months </em>the pine tree was expected to grow.
The y-axis represents the <em>Height of the Tree </em>in inches.

Since the slope o a line is:

$Slope=\frac{Change \ in \ y}{Change \ in \ x}=\frac{2}{3}$

Then, this means that<em> every three months the pine tree grows two inches, </em><em>or </em><em>for every month the pine tree grows about 0.67 inches.</em>

The y-intercept can be found setting $x=0$ . So, from our equation: