Use a graphing utility to graph the equation of the line in...

Use a graphing utility to graph the equation of the line in the form
$\frac{x}{a}+\frac{y}{b}=1, \quad a \neq 0, b \neq 0$.
Use the graphs to make a conjecture about what a and b represent. Verify your conjecture.
$\frac{x}{5}+\frac{y}{-3}=1$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Intercept form of a line

The intercept form of a line, expressed as x/a + y/b = 1, makes it explicit that the line crosses the x-axis at (a, 0) and the y-axis at (0, b). This format is useful for quickly identifying where the line intersects the axes, which is a fundamental aspect of linear equations in coordinate geometry.

X-intercept

The x-intercept of a line is the point at which it crosses the x-axis, which occurs when y is equal to zero. In the intercept form x/a + y/b = 1, setting y = 0 immediately gives x = a, showing that a represents the x-intercept of the line.

Y-intercept

Similarly, the y-intercept is the point where the line crosses the y-axis, which happens when x is equal to zero. In the intercept form x/a + y/b = 1, setting x = 0 directly results in y = b, indicating that b is the y-intercept of the line.

Graphing utility

A graphing utility is a tool that allows for the visual representation of functions and equations. It can be used to plot the line given by the equation in intercept form, thereby helping to validate the conjecture that a and b are the coordinates where the line intersects the x-axis and y-axis, respectively.

Transcript

Please give Ace some feedback