One number is 2 less than a second number. twice the second number is 16 more than 4 times the first. find the two numbers.

1 answer:

4 0

Let the numbers be x and y

x= y-2.... (1)
and, 2y = 16 + 4x.... (2)

putting the value of x from (1) in (2),

2y = 16 + 4x
=> 2y = 16 + 4(y-2)
=> 2y = 16 + 4y - 8
=> 2y = 8 + 4y
=> 2y - 4y = 8
=> -2y = 8
=> y =-8/2
=> y= -4

and x = -4-2 = -6

hence , in short the numbers are -2 and -4

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Determine the standard form of the equation of the line that passes through (6, -9) and (-8, 6)

horrorfan [7]

9514 1404 393

Answer:

A. 15x +14y = -36

Step-by-step explanation:

Since we are given two points, we can start with the 2-point form of the equation for a line.

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

y = (6 -(-9))/(-8 -6)(x -6) +(-9)

y = 15/-14(x -6) -9

Multiplying by -14, we have ...

-14y = 15x -90 +126

Adding 14y-36 to both sides gives ...

-36 = 15x +14y . . . . matches choice A

The standard-form equation is ...

15x +14y = -36

_____

<em>Additional comments</em>

It can be easier to start with the form ...

(Δy)x -(Δx)y = (Δy)x1 -(Δx)y1 . . . . . where Δx = x2-x1 and Δy = y2-y1

This gives ...

(6+9)x -(-8-6)y = 15(6) +14(-9)

15x +14y = -36 . . . simplified

You can also start with the slope-intercept form or the point-slope form, if you're more familiar with those. The result will be the same. I find it handy to be familiar with a number of different forms of the equation for a line.