Respuesta :

mathmate
The graph has no scale, so we can only make conclusions based on:
1. slope is negative (true), zero, or positive
    slope is coefficient of x when equation is in standard form
2. y-intercept is negative, zero, or positive (true)
    y-intercept is value of y when x=0
3. x-intercept is negative, zero, or positive (true).
    x-intercept is value of x when y=0




Now let's look at the given answer choices:
A. 2x-y=7 => y=2x-7  => slope=2 >0 (false); => FALSE
B. 3x+2y=6 => y=-1.5x+6 => slope<0 (true); y-intercept>0 (true); x-intercept=6/3=2 >0 (true)  => TRUE
C. y=5 => slope=0 (false) => FALSE
D. y=-4x+2 => slope=-4 <0  (true); y-intercept=2>0 (true); x-intercept=+1/2>0 (true) => TRUE

Option B and D are suitable for the equation of the graph shown.

What is slope-intercept form of a line?

The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis). The slope intercept form is a method used to determine the equation of a straight line in the coordinate plane.

By observing the graph

Graph is going down. So the slope is negative

y-intercept is positive value because it is above x-axis.

Given

Option A :

2x - y = 7

⇒ y = 2x - 7

This equation has negative y-intercept and positive slope

Option B:

3x + 2y = 6

⇒ 2y = 6 - 3x

⇒ y = [tex]\frac{-3}{2}x +3[/tex]

This equation has positive y-intercept and negative slope.

Option C:

y = 5

It has only positive y -intercept.

Option D:

y = -4x + 2

This equation has positive y-intercept and negative slope.

Find out more information about slope-intercept form here

https://brainly.com/question/9682526

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