Answer:
y = -1/3x + 14/3
Step-by-step explanation:
We have the standard equation as;
y = mx + b
where m is the slope and b is the y-intercept
the given points are;
(-1,5) and (2,4)
So we plug x and y for each of the points
then we create two linear equations which we can solve simultaneously to get the values of m and b
From the points;
5 = -m + b•••••••(i)
4 = 2m + b
from i;
b = 5 + m
substitute this into equation ii
4 = 2m + 5 + m
4 = 3m + 5
4-5 = 3m
3m = -1
m = -1/3
Recall;
b = 5 + m
b = 5-1/3
b = 14/3
so we have the equation as;
y = -1/3x + 14/3
Multiply through by 3
3y = -x + 14
Look at where the lines intersect each other, if they do then you can use one of the coordinates. the lines that don’t touch means no solution
3x+2(x-1)=9x=4
We move all terms to the left:
3x+2(x-1)-(9x)=0
We add all the numbers together, and all the variables
-6x+2(x-1)=0
We multiply parentheses
-6x+2x-2=0
We add all the numbers together, and all the variables
-4x-2=0
We move all terms containing x to the left, all other terms to the right
-4x=2
x=2/-4
x=-1/2
Graph C is the correct option.
If you drew a straight line (mostly) connecting the points, it would be linear. A relationship is linear if one variable, in this case, x, increases by approximately the same rate as the other variables, in this case y.
If you drew lines connecting points on the other graphs, they wouldn’t resemble a straight line, therefore, they aren’t linear.
