Question

write an equation that demonstrates the relationship between x and y for the points plotted on the coordinate grid

Answer 1

The relationship between x and y points is a linear relationship of the form:

y = mx + b

where m is the slope of the line, and b is the coordinate y for the y-intercept.

Now, by definition, we have that the slope of the line is given by:

$m\text{ = }\frac{Y2-Y1}{X2-X1}$

where (X1,Y1) and (X2,Y2) are given points on the graph.

In our case, we can take

(X1, Y1) =(2,-1)

(X2,Y2) = (3,2)

then, te slope of the line would be:

$m\text{ = }\frac{Y2-Y1}{X2-X1}\text{ = }\frac{2-(-1)}{3-2}\text{ = }\frac{2+1}{1}=\text{ 3}$

then m = 3 and the new equation for our graph would be:

y = 3x+b

Now, to find b, take any point (x,y) on the graph. In this case, for example

(x,y) = (3,2) and replace this point in the above equation:

2= 3(3) + b

solve for b:

2-9 = b

then b = -7 and we can conclude that the equation for our graph is:

y = 3x-7