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2 years ago

The equation of a line is y = 1.5x − 2. What are its slope and y-intercept?

Mathematics

2 answers:

allochka39001 [22]2 years ago

6 0

Answer: The slope of the line is 1.5 and the y-intercept is -2.

Step-by-step explanation: We are given that the equation of a straight line is as follows :

$y=1.5x-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the slope and y-intercept of the given line.

We know that

the slope-intercept form of the equation of a straight line is given by

$y=mx+c,$ where m is the slope and c is the y-intercept of the line.

From equation (i), we have

$y=1.5x-2\\\\\Rightarrow y=1.5x+(-2).$

Comparing the above equation with the slope-intercept form, we get

slope, m = 1.5 and y-intercept, c = -2.

Thus, the slope of the line is 1.5 and the y-intercept is -2.

irakobra [83]2 years ago

4 0

Slope: 1.5
y-intercept: -2

Explanation:
The slope is the number attached to 'x' in the equation. In this case, 1.5 would be the slope because it's attached to x.

The y-intercept is the constant the number not attached to any variables. In this case, -2 is all by itself.

Hope that helps!

:D®

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Earth, Mars, Saturn, Uranus and Neptune revolve around the sun. Earth takes 1 year, Mars 2 years, Saturn 30 years, Uranus 84 yea

Anettt [7]

Answer:

30 years

Step-by-step explanation:

2 is a factor of 30, so the LCM of 2 and 30 is 30.

Saturn and Mars will appear in the same direction in the night sky every 30 years.

3 0

2 years ago

Write a rule to describe the function shown. x y −6 −4 −3 −2 0 0 3 2 y equals start fraction two over three end fraction x y equ

sertanlavr [38]

Answer:

$y=\frac{2}{3} x$ (y equals start fraction two over three end fraction x)

Step-by-step explanation:

Lest's organize the table values of our function first:

x y

-6 -4

-3 -2

0 0

3 2

The simplest kind of of function is a linear function of the form $y=mx+b$ where $m$ is the slope and $b$ is the y-intercept. Let's us check if our function is a linear one finding its equation and checking that all points are in the line.

The first step to find a linear equation is find the slope of the line; to do it, we are using the slope formula:

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

where

$m$ is the slope of the line

$(x_1,y_1)$ are the coordinates of the first point

$(x_2,y_2)$ are the coordinates of the second point

We know from our table that the first and second points are (-6, -4) and (-3, -2) respectively, so $x_1=-6$ , $y_1=-4$ , $x_2=-3$ , and $y_2=-2$ .

Replacing values:

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

$m=\frac{-2-(-4)}{-3-(-6)}$

$m=\frac{-2+4}{-3+6)}$

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

Now that we have the slope of our line we can use the point slope formula to complete our linear function:

$y-y_1=m(x-x_1)$

where

$m$ is the slope

$(x_1,y_1)$ are the coordinates of the first point

Replacing values:

$y-y_1=m(x-x_1)$

$y-(-4)=\frac{2}{3)}(x-(-6))$

$y+4=\frac{2}{3)}(x+6)$

$y+4=\frac{2}{3} x+4$

$y=\frac{2}{3} x+4-4$

$y=\frac{2}{3} x$

Now, to check if our function is valid, we can either check if each point satisfies the rule $y=\frac{2}{3} x$ , or we can graph it and check if each lies is in the graph.

Let's check both:

We already know that points (-6, -4) and (-3, -2) satisfy the rule (after all, those were the point we used to came out with the rule in the first place), so we just need to check the points (0, 0) and (3, 2)

- For (0, 0):

$y=\frac{2}{3} x$

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

$0=0$

The point satisfies the rule.

- For (3, 2):

$y=\frac{2}{3} x$

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

$2=2$

The point satisfies the rule.

Since all the points of our table satisfies the rule $y=\frac{2}{3} x$ , we can conclude that the rule describing the function shown is $y=\frac{2}{3} x$ .

4 0

3 years ago

Read 2 more answers

What is the coefficient of the second term of the trinomial?

marin [14]

The coefficient of the second term is 18.

What you do is you FOIL the terms:
$(3x+3)(3x+3)\\ Multiply\ the\ first\ terms\ together:\\ 3x*3x=9x^{2}\\ Then\ the\ outer\ terms:\\ 3x*3=9x\\ Next,\ the\ inner\ terms:\\ 3x*3=9x\\ Finally,\ multiply\ the\ last\ terms:\\ 3*3=9\\ Putting\ the\ terms\ together:\\ 9x^{2}+9x+9x+9=9x^{2}+18x+9\\\\ Since\ (3x+3)^{2}=9x^{2}+Bx+9=9x^{2}+18x+9,\ then \ B=18.$