The points ( − 1.6 , 2.6 ) and ( 3.4 , 9.1 ) are on the graph of a linear relationship between two variables, x and y .

Question

The points  and  are on the graph of a linear relationship between two variables,  and .

What is the constant rate of change of  with respect to ?

Write a formula that expresses 

 in terms of 

.

What is the value of 

 when 

?

Answer 1

Hi Mark,

when the points are on the graph of a linear relationship between the 2 variables, y and x,

the constant rate of change of y with respect to x is the slope of the line (m),

m = change in y / change in x (or rise/run)

with the 2 points (-1.6, 2.6) and (3.4, 9.1),

m = (9.1 - 2.6) / (3.4 - -1.6) = 1.3

in terms of x, y = mx + b, m is the slope, b is the y-intercept

y = 1.3x + b

we can use one the point to find b, let us use (3.4, 9.1)

9.1 = 1.3*3.4 + b => b = 4.68

so y = 1.3x + 4.68

To find the value of y when x = 113, you just plug x into the above equation,

y = 1.3*113 + 4.68 = 151.58

Hope this helps!

Answer 2

The rate of change of y with respect to x is also called the slope of the line, usually expressed as m.

m= (y2-y1)/(x2-x1). In this case, m=(9.1-2.6)/[ 3.4 - (-1.6) ] = 6.5/5.0 = 1.3

To find the equation of the line, use the point/slope formula. Given a point on the line (x1, y1) and the slope m,

the equation of the line is given by (y-y1) = m*(x-x1). Since both of the given points lie on the line, you can use either one, along with the slope m=1.3.

y-9.1= 1.3*(x-3.4)

Simplify to get y-9.1 = 1.3x - 4.42

Add 9.1 to both sides to get the final answer of y= 1.3x + 4.68