Question

juanita makes leather lanyards to sell she charges a base fee and a cost per inch of the finished lanyard.

Answer 1

y = ½x + 5

If y is the total amount Juanita makes for x inches of finished lanyard,

Base fee = y-intercept = 5

Cost per inch = Slope = 0.5 = ½

Step-by-step explanation

To write the expression for this, we need to write the equation for the line representing the whole function

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

y = mx + b

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.

b = y-intercept of the line.

From the gaph, we can easily see that

b = y-intercept = point where the line crosses the y-axis = 5

For the slope, 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}}=(y_2-y_1)/(x_2-x_1)`

For this question,

(x₁, y₁) and (x₂, y₂) are (2, 6) and (6, 8)

`\text{Slope = }(8-6)/(6-2)=(2)/(4)=(1)/(2)=0.5`

Recall,

y = mx + b

m = slope = 0.5 = ½

b = y-intercept = 5

y = ½x + 5

If y is the total amount Juanita makes for x inches of finished lanyard,

Base fee = y-intercept = 5

Cost per inch = Slope = 0.5 = ½

Hope this Helps!!!