Answer:
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
<u>The statement is true</u>
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
<u>The statement is true</u>
Because the slope is positive (is an increasing function)
case e) The x-intercept is 0
<u>The statement is true</u>
Because in a proportional relationship the x-intercept and the y-intercept are equal to zero