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The coordinate plane is a two-dimensional surface on which we can plot points, lines, and curves. It is defined by two number lines that intersect at a right angle. These number lines are known as the x-axis (horizontal) and the y-axis (vertical). The point where they intersect is called the origin, which has the coordinates

• (0, 0).

Each point on the plane is identified by a pair of numbers written as

• (x, y).

Here, 'x' represents the horizontal position, and 'y' represents the vertical position.

When graphing linear equations like

• \( y = -x + 2 \),

we plot points on the coordinate plane to create a visual representation. To find these points, we select different x-values, compute the corresponding y-values, and use these as coordinates on the plane. By connecting these points with a straight line, we represent solutions to the linear equation.

A linear equation is an equation that creates a straight line when graphed. It takes the general form of

• \( y = mx + b \),

where 'm' is the slope and 'b' is the y-intercept. In our equation of

• \( y = -x + 2 \),

this form allows us to quickly identify the slope and the y-intercept. Linear equations depict a constant rate of change and show a linear relationship between two variables, 'x' and 'y'.

To graph a linear equation, we must find two or more points on a coordinate plane and plot them. For each chosen x-value, substitute it into the equation to solve for the corresponding y-value. These solutions are points that lie on the line. Once you have at least two points, draw a line through them. For the equation \( y = -x + 2 \), the points (0, 2) and (2, 0) are solutions that lie on this line.

The slope-intercept form of a linear equation is one of the most common and intuitive ways to represent a linear function. This form is written as

• \( y = mx + b \).

Here, 'm' denotes the slope of the line, while 'b' represents the y-intercept. The slope (m) indicates the steepness and direction of the line; it measures the change in y for every unit change in x. In our example of

• \( y = -x + 2 \),

the slope is

• -1,

showing a decrease in y by 1 unit for each unit increase in x.

The y-intercept (b) is the point where the line crosses the y-axis. This is where x equals zero. For the equation \( y = -x + 2 \), the y-intercept is

• 2,

illustrating that the line crosses the y-axis at the point (0, 2). This format allows for easy graphing and understanding of how variables in the equation interact.