91Ó°ÊÓ

A coordinate plane is a two-dimensional surface on which we can plot points, lines, and curves. It consists of two number lines that intersect at a right angle. The horizontal line is known as the x-axis, and the vertical line is known as the y-axis. These axes divide the plane into four quadrants.

The intersection of the x-axis and y-axis is called the origin, which has the coordinates (0,0). Each point on the plane is defined by a pair of numbers known as coordinates, written as (x,y), where x represents the horizontal position and y represents the vertical position.

Understanding the coordinate plane is crucial for graphing linear equations and determining if specific points lie on a line. In our given exercise, we are verifying if the points (1.4, -1.05) and (0, -1.75) are on the graph of the line represented by the equation. The coordinate plane provides the visual aid to view such graphs and points.

The substitution method is a straightforward technique for solving equations, particularly useful for checking if certain points lie on the line represented by a linear equation.

To use this method, follow these steps:

• Take the coordinates of the point in question, which is given in the form (x, y).
• Substitute these x and y values into the linear equation.
• Simplify to see if the actual equation holds true (results in an identity like 7 = 7 in our example).

By substituting the values, you're essentially checking if the equation balances. If it does, the point indeed lies on the line. For example, after substituting (1.4, -1.05) into the equation \[2x - 4y = 7\], we find that it holds true. This means the point is on the line. Similarly, we verify point (0, -1.75). This method helps in understanding the consistency of the point with the equation's graph.

When we talk about points on a graph, we refer to specific locations on the coordinate plane that have definite x and y coordinates. These points can help illustrate the relationship described by an equation.

A linear equation, like \[2x - 4y = 7\], typically forms a straight line when graphed. If a point lies on this line, it means substituting the point's coordinates into the equation will result in a true statement.

• To determine the position of a point, take its coordinates (x, y).
• Plot these on the graph, using the x-axis for the x-value and the y-axis for the y-value.
• If the point is on the line, it will fall exactly on this graphed line.

In our exercise, both points, (1.4, -1.05) and (0, -1.75), lie on the graph of the equation. This confirmation comes from the fact that they satisfy the equation, validating their alignment on the graph. Points on a graph provide visual and analytical confirmation of the relationships expressed by the linear equation.