Answer:
A. [tex]y =\frac{7}{8}x+1[/tex]
B. [tex]y = -10x[/tex]
C. [tex]y = 2.5x - 7[/tex]
D. [tex]y = 1.2x[/tex]
E. [tex]y = -5x -8[/tex]
Step-by-step explanation:
Let the descriptions be A to E.
First, we need to note the followings.
An equation is of the form
[tex]y = mx + b[/tex]
[tex]m = slope[/tex] and [tex]b = y\ intercept[/tex]
A. Non proportional graph with positive y intercept
From the list of options, only
The slope of [tex]y =\frac{7}{8}x+1[/tex] is positive
and y intercept is also positive
B. Negative slope and pass through the origin.
Negative slope means m is negative
From the list of options
[tex]y = -10x[/tex] and [tex]y = -5x -8[/tex]
Origin implies (0,0)
i.e: [tex]x = 0[/tex] and [tex]y = 0[/tex]
For y = -10x
[tex]0 = -10 * 0[/tex]
[tex]0 = 0[/tex] --- This is true
For [tex]y = -5x -8[/tex]
[tex]0 = -5 * 0 - 8[/tex]
[tex]0 = 0 - 8[/tex]
[tex]0 = -8[/tex] --- This is not true
Hence:
[tex]y = -10x[/tex] fits this description
C. Increases from left to right and b is negative
For b is negative, we have the following:
[tex]y = -5x -8[/tex] and
[tex]y = 2.5x - 7[/tex]
An increment from left to right, means the slope is positive.
So, we have:
[tex]y = 2.5x - 7[/tex]
D. Positive slope and contains (0,0)
From the options, we have the following functions left:
[tex]y = -5x -8[/tex] and
[tex]y = 1.2x[/tex]
But [tex]y = 1.2x[/tex] has a positive slope and also contain (0,0) because
[tex]0 = 1.2 * 0[/tex]
[tex]0 = 0[/tex]
E. Negative m and Negative b
[tex]y = -5x -8[/tex] has these descriptions
