Question

Graph each linear equation. $4 x+y=7$

   Graph each linear equation.
$4 x+y=7$

Intermediate Algebra

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 3, Problem 3

Instant Answer

Solved by Expert Kyler Gray

07/16/2020

Step 1

To do this, we subtract $4x$ from both sides of the equation to isolate $y$ on one side. This gives us: \[y = -4x + 7\] Show more…

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Graph each linear equation. $4 x+y=7$

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Key Concepts

Linear Equation

A linear equation represents a relationship between two variables that produces a straight line when graphed on a coordinate plane. It is typically written in forms like Ax + By = C or y = mx + b, where the variables interact in a linear (first-degree) manner.

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where 'm' denotes the slope, indicating the line's steepness and direction, and 'b' is the y-intercept, the point where the line crosses the y-axis. This form is especially useful for graphing.

Slope

The slope is the measure of the steepness or incline of a line, calculated as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run). It determines how much the value of y changes for a unit increase in x.

Y-intercept

The y-intercept is the point where a line crosses the y-axis (i.e., where x equals zero). It provides a starting value for plotting the graph of the line, as it indicates the value of y when x is zero.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation and drawing a line through these points. This process typically uses the key features of the equation, such as the slope and y-intercept, to accurately depict the line on the coordinate plane.

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