Question

Find the intercepts for each equation. $3 x-2 y=12$

   Find the intercepts for each equation.
$3 x-2 y=12$

Elementary Algebra

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 4, Problem 169

Instant Answer

Solved by Expert Karla Conrey

07/17/2021

Step 1

The equation becomes: \[3x - 2(0) = 12\] which simplifies to: \[3x = 12\] Show more…

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Find the intercepts for each equation. $3 x-2 y=12$

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Key Concepts

Y-intercept

The y-intercept is the point where the graph crosses the y-axis. To find the y-intercept, one sets the x-value to zero and solves the equation for y. This intercept gives insight into the starting value or initial condition of the function when graphed.

X-intercept

The x-intercept is the point where the graph of an equation crosses the x-axis. To determine the x-intercept, one sets the y-value to zero and solves the equation for x, thereby finding the specific point along the x-axis at which this occurs.

Intercepts

Intercepts are the points where a graph crosses the axes. They provide critical information about the behavior of the graph and serve as reference points when plotting or analyzing the equation. The two main types are the x-intercept and the y-intercept.

Linear Equation

A linear equation in two variables represents a straight line on a Cartesian plane and is typically expressed in forms such as standard form or slope-intercept form. Understanding linear equations is essential for grasping relationships between variables and analyzing how changes in one variable affect another.

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