Graph a line through the origin that has a slope of -4/3

The line goes the through the origin

The line is sloping upward

The x-intercept is 0

Step-by-step explanation:

step 1

Find the equation of the line in point slope form

we have

substitute

step 2

Convert to slope intercept form

isolate the variable y

Applying the distributive property right side

The line represent a direct variation (the line passes though the origin)

step 3

Verify each statement

case a) The line is horizontal

The statement is false

Because a horizontal line has a slope equal to zero and this line has slope equal to m=3/4

case b) The line goes the through the origin

The statement is true

Because the line represent a direct variation

case c) The point (3,4) lies on the line

The statement is false

Because the ordered pair not satisfy the equation

Verify

For x=3, y=4

substitute in the equation

> is not true

so

the ordered pair not satisfy the equation

therefore

The ordered pair not lies on the line

case d) The line is sloping upward

The statement is true

Because the slope is positive (is an increasing function)

case e) The x-intercept is 0

The statement is true

Because in a proportional relationship the x-intercept and the y-intercept are equal to zero

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step-by-step explanation: