Question

1. The value of y varies directly with x, and y = 48 when x = 16. Find y when x = 176.
y = 3
y = 368
y = 58.7
y = 528
2.Write an equation in slope-intercept form of the line with slope 3/4 that contains the point (−4,1).


y=3/4x+3

y=3/4x+1

y=3/4x−4

y=3/4x+4
3. Tell whether the equation 4x + y = 3 represents a direct variation. If so, identify the constant of variation.
Direct variation, k = −1/4
Direct variation, k = 3
Direct variation; k = −4
Not a direct variation.

PLEASE HELP ME!!

Answer 1

Answer:

Part 1) $y=528$

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

Part 3) Not a direct variation

Step-by-step explanation:

Part 1) we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In this problem we have

$y=48, x=16$

Find the constant of proportionality k

$y/x=k$

substitute the values

$48/16=k$

$k=3$

The equation of the direct variation is equal to

$y=3x$

so

For $x=176$

$y=3(176)=528$

Part 2) we know that

the equation of the line in slope-intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

we have

$m=\frac{3}{4}$

Point $(-4,1)$

substitute the values in the equation and solve for b

$1=\frac{3}{4}(-4)+b$

$1=-3+b$

$b=4$

the equation is equal to

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

Part 3) Tell whether the equation $4x + y = 3$ represents a direct variation

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In the direct variation the constant of proportionality k is equal to the slope of the line and the line passes through the origin

In the linear equation  $4x + y = 3$ the line does not passes through the origin

so

Not a direct variation