In Exercises 105-108, use the results of Exercises 101-104 to write an equation of the line that

step 1 Okay, so we want to use our results from exercises 91 to 94 to write an equation of our line tha

In Exercises 105-108, use the results of Exercises 101-104...

Key Concepts

Intercepts

Intercepts are the points where a line crosses the coordinate axes. The x-intercept is where the line crosses the x-axis (and the y-coordinate is 0), and the y-intercept is where the line crosses the y-axis (and the x-coordinate is 0). These points are critical for quickly understanding and graphing the behavior of linear equations.

Slope

The slope of a line indicates its steepness and direction. It is calculated as the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. Understanding slope is essential for forming the equation of a line and analyzing how quickly one variable changes with respect to another.

Slope-Intercept Form

The slope-intercept form is a way of expressing the equation of a line as y = mx + b, where m represents the slope and b represents the y-intercept. This form is especially useful because it immediately reveals the slope and the point where the line crosses the y-axis, simplifying both graphing and interpretation of the line's behavior.

Equation of a Line

Writing the equation of a line involves determining the slope and using one of the intercept points, or another point on the line, to express the line in a chosen form such as the slope-intercept form or the point-slope form. This process is fundamental in algebra and calculus for modeling linear relationships between variables.

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