Answer :
Answer:
y < –3x + 4
Step-by-step explanation:
Finding the Equation of the Line
The equation for a line is,
y = mx + b,
where m is the slope and b is the y-intercept.
The slope can be found by taking two points on the line and plugging them into the slope formula:
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex],
where the subscripts indicate from which point the value originates.
Letting [tex](x_2,y_2)=(0,4)[/tex] and [tex](x_1,y_1)=(1.3,0)[/tex],
[tex]\dfrac{4-0}{0-1.3}=-3.07 \approxeq -3[/tex].
So our equation is now,
y = -3x + b.
To find b--the y-value of the y-intercept--we can either plug one of the points into the equation and rearrange for b or take a shortcut.
All y-intercepts have an x value of 0, knowing this we can identify that one of the points given to us is the y-intercept: (0, 4). So, b = 4.
Our equation is
y = -3x + 4,
eliminating the top two answer choices.
[tex]\dotfill[/tex]
Determining the Inequality Sign
If the inequality leaves the left region of the line shaded, we can plug a point that we know is left of this line into both equations to see which is satisfied.
Given that both of the points provided in the problem are adjacent to the first quadrant, we know that it is to the right of the origin, making the origin a part of the left region that our problem describes.
Plugging (0,0) into the last two candidates we have:
0 > -3(0) + 4 --> 0 > 4 (False)
0 < -3(0) + 4 --> 0 < 4 (True)
Because the last answer choice is satisfied by this coordinate point, it must be our answer.
