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.

Part 1)

Part 2)

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 or

In this problem we have

Find the constant of proportionality k

substitute the values

The equation of the direct variation is equal to

so

For

Part 2) we know that

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

where

m is the slope

b is the y-coordinate of the y-intercept

we have

Point

substitute the values in the equation and solve for b

the equation is equal to

Part 3) Tell whether the equation 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 or

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   the line does not passes through the origin

so

Not a direct variation