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
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{4}[/tex]
[tex]point\ (-4,-3)[/tex]
substitute
[tex]y+3=\frac{3}{4}(x+4)[/tex]
step 2
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
Applying the distributive property right side
[tex]y+3=\frac{3}{4}x+3[/tex]
[tex]y=\frac{3}{4}x[/tex]
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
[tex]4=\frac{3}{4}(3)[/tex]
[tex]4=\frac{9}{4}[/tex] ----> 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
