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ratelena [41]
3 years ago
5

Find the nth term of this sequence 7, 10, 13, 16...

Mathematics
1 answer:
Finger [1]3 years ago
3 0

Answer:

3n+4 or n3+4

Step-by-step explanation:

7,10,13,16

they all have a difference of 3

so that's 3n

start with the first one: 3(1)+?=7

7-3=4

3n+4

use this for the other ones to double check

3(2)+4

6+4=10

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A line passes through the point (–6, –3) and has a slope of 2/3 . Which point is on the same line?
navik [9.2K]

Answer:

The point (0, 1) represents the y-intercept.

Hence, the y-intercept (0, 1) is on the same line.

Step-by-step explanation:

We know that the slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given

  • The point (-6, -3)
  • The slope m = 2/3

Using the point-slope form

y-y_1=m\left(x-x_1\right)

where

  • m is the slope of the line
  • (x₁, y₁) is the point

In our case:

  • m = 2/3
  • (x₁, y₁) = (-6, -3)

substituting the values m = 2/3 and the point (-6, -3)  in the point-slope form

y-y_1=m\left(x-x_1\right)

y-\left(-3\right)=\frac{2}{3}\left(x-\left(-6\right)\right)

y+3=\frac{2}{3}\left(x+6\right)

Subtract 3 from both sides

y+3-3=\frac{2}{3}\left(x+6\right)-3

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

y=\frac{2}{3}x+1

comparing with the slope-intercept form y=mx+b

Here the slope = m = 2/3

Y-intercept b = 1

We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

Given the line

y=\frac{2}{3}x+1

at x = 0, y = 1

Thus, the point (0, 1) represents the y-intercept.

Hence, the y-intercept (0, 1) is on the same line.

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