Question 301230
Use the direct variation formula of y = k*x


Solve for k first using the known values of x and y.


Let x = 2 and y = 8.4


Formula becomes:


8.4 = k*2


Divide both sides of this equation by 2 to get:


k = 4.2


k winds up being the slope of your straight line equation.


The formula for a straight line equation is y = m*x + b


m is the slope and b is the y-intercept.


The slope is 4.2.


The y-intercept is found by substituting known values for x and y in the equation and solving for b.


the known values are (x,y) = (2,8.4)


Equation of y = 4.2*x + b becomes 8.4 = 4.2*2 + b which becomes 8.4 = 8.4 + b.


Solve for b to get b = 0.


Your straight line equation is y = 4.2*x


Graph this equation to get:


{{{graph(600,600,-5,5,-20,20,4.2*x,8.4,14.7)}}}


Horizontal line at y = 8.4 intersects the graph of the equation of the line at x = 2.


Horizontal line at y = 14.7 intersects the graph of the equation of the lin at x = 3.5.


This confirms the equation is good.   


When x = 2, y = 8.4


When x = 3.5, y = 14.7


The rate of change is the slope of the line which is 4.2.


This means that for every change of 1 in the value of x, y changes by 4.2.