Question

The graph below shows a linear relationship. The points shown have whole-number coordinates. 9 8 7 6 5 -1 1 3 1 2 3 4 5 6 7 8 9 0 1 2 -3 4 5 -6 -7 8 9

Answer 1

Answer

The linear relationship between y and x is

y = (2x/3) + 2

Explanation

This is a straight line, that we can just solve for the linear relationship by solving the equation of this straight line.

The slope and y-intercept form of the equation of a straight line is given as

y = mx + c

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

c = y-intercept of the line.

So, we just need to solve for the slope and the y-intercept.

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

$Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}$

For this question,

(x₁, y₁) and (x₂, y₂) are (-3, 0) and (0, 2)

$\text{Slope = }\frac{2-0}{0-(-3)}=\frac{2}{0+3}=\frac{2}{3}$

Then, the y-intercept is where the line crosses the y-axis

c = y-intercept = 2

y = mx + c

y = (2/3)(x) + 2

y = (2x/3) + 2

Hope this Helps!!!