# Word Problem for slope intercept graph equation

• MHB
• mhester88
In summary, the problem involves finding the equation for the data and calculating the shipping rate. The cost function is represented by the ordered pair $(w, c)$ where $w$ is the weight and $c$ is the cost. To find the cost function, you need to find the slope between two given points and use the point-slope form of a linear equation. The equation can be written as $c-c_1 = m(w-w_1)$ where $m$ is the slope and $(w_1, c_1)$ is a point on the line. Then, use the given points to solve for $a$ and $b$ in the equation $c= aw + b$.
mhester88
I have this word problem that is asking for two different answers, the equation for the data and to calculate the shipping rate. I'm not understanding how to address either of the questions. Will someone please help me with this answer?

shipping cost is dependent on weight

an ordered pair for the cost function would be $(w, c)$ where $w$ is the weight (the independent variable), and $c$ is the cost (the dependent variable

you are given two such ordered pairs, $(4, 3.55)$ and $(6, 4.35)$

find the slope between those two given points, then use the point-slope form of a linear equation to get the cost function

Thank you for your response. If I'm understanding this correctly, then the slope would be 0.4. I'm still confused on how to write the equation using c and w. I'm not sure how to even begin creating the equation.

mhester88 said:
Thank you for your response. If I'm understanding this correctly, then the slope would be 0.4. I'm still confused on how to write the equation using c and w. I'm not sure how to even begin creating the equation.

point-slope form of a linear equation ...

$y - y_1 = m(x - x_1)$

where $(x_1,y_1)$ is a point on the line and $m$ is the slope

... requires one point (you have two), and the slope, $m$.

remember, y is the cost (you can use c instead) and x is the weight (you can use w instead)

$c - c_1 = m(w - w_1)$

Any (non-vertical) line has equation c= aw+ b for some numbers, a and b. You are told that when the weight, w, is 4 lb. the cost, c, is \$3.55 so 3.55= a(4)+ b. You are told that when the weight, w, is 6 lb. the cost, c, is \$4.35 so 4.35= a(6)+ b.

Solve the two equations, 4a+ b= 3.55 and 6a+ b= 4.35, for a and b. I recommend you subtract the first equation from the second to eliminate b.

## 1. What is a slope intercept graph equation?

A slope intercept graph equation is a linear equation in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept (the point where the line crosses the y-axis).

## 2. How do you graph a slope intercept equation?

To graph a slope intercept equation, plot the y-intercept point (b) on the y-axis. Then, use the slope (m) to find additional points on the line by moving up or down (based on the sign of m) and right or left (based on the value of m) from the y-intercept. Finally, connect all the points to create the line.

## 3. What is the significance of the slope in a slope intercept equation?

The slope represents the rate of change of the line. It tells us how much the y-value changes for every unit change in the x-value. A positive slope indicates an upward trend, while a negative slope indicates a downward trend.

## 4. How do you calculate the slope of a line from two points?

To calculate the slope of a line from two points, use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

## 5. Can a slope intercept equation have a horizontal or vertical line?

Yes, a slope intercept equation can have a horizontal or vertical line. A horizontal line has a slope of 0 and a vertical line has an undefined slope (denoted as "undefined" or "no slope").

Replies
2
Views
978
Replies
4
Views
949
Replies
5
Views
2K
Replies
14
Views
964
Replies
16
Views
2K
Replies
5
Views
2K
Replies
4
Views
2K
Replies
3
Views
2K
Replies
2
Views
2K
Replies
8
Views
3K