How do you use slope and intercept to model real-world scenarios?

1 What is slope?

Slope is a measure of how steep a line is, or how fast one variable changes as another variable changes. It is calculated by dividing the vertical change (rise) by the horizontal change (run) between any two points on the line. For example, if you have a line that passes through the points (2, 4) and (6, 10), the slope is (10 - 4) / (6 - 2) = 1.5. This means that for every unit increase in the horizontal variable (x), the vertical variable (y) increases by 1.5 units.

2 What is intercept?

Intercept is the value of the vertical variable (y) when the horizontal variable (x) is zero, or the point where the line crosses the y-axis. It is also called the y-intercept or the constant term of the linear equation. For example, if you have a line with the equation y = 2x + 5, the intercept is 5. This means that when x is zero, y is 5.

3 How to write a linear equation?

A linear equation is an equation that describes a straight line with a constant slope and intercept. The most common form of a linear equation is y = mx + b, where m is the slope and b is the intercept. To write a linear equation, you need to know either the slope and intercept, or two points on the line. If you know the slope and intercept, you can simply plug them into the equation. If you know two points on the line, you can use them to find the slope and then use one of them to find the intercept.

4 How to graph a linear equation?

A graph is a visual representation of a linear equation, where the horizontal axis (x-axis) and the vertical axis (y-axis) show the values of the variables. To graph a linear equation, you need to plot at least two points on the line and then connect them with a straight line. You can use the slope and intercept to find the points, or use the points to find the slope and intercept. For example, if you have the equation y = 2x + 5, you can use the intercept to plot the point (0, 5) and then use the slope to find another point by adding 2 to y and 1 to x, which gives you (1, 7). Then you can draw a line through these points.

5 How to make a table from a linear equation?

A table is another way of showing the relationship between two variables in a linear equation. It lists the values of the horizontal variable (x) and the corresponding values of the vertical variable (y) in rows and columns. To make a table from a linear equation, you need to choose some values for x and then use the equation to calculate the values for y. For example, if you have the equation y = 2x + 5, you can choose x = -2, -1, 0, 1, 2 and then find y by plugging them into the equation:

x | y

-2 | 1

-1 | 3

0 | 5

1 | 7

2 | 9

6 How to use slope and intercept to model real-world scenarios?

Slope and intercept can help you model real-world scenarios by showing how one variable depends on another variable in a linear way. For example, if you want to model how the cost of renting a car depends on the number of days, you can use a linear equation with slope and intercept. The slope represents the rate of change of the cost per day, and the intercept represents the fixed fee or deposit. If you know that renting a car costs $25 per day plus a $100 deposit, you can write the equation as y = 25x + 100, where y is the cost and x is the number of days. You can then use the equation, graph, or table to find the cost for any number of days, or the number of days for any cost.