In the context of linear equations, which of the following statements best describes the relationship between the coefficients and the solutions of the equations?
Practice Questions
1 question
Q1
In the context of linear equations, which of the following statements best describes the relationship between the coefficients and the solutions of the equations?
The coefficients determine the slope and intercept of the line.
The solutions are independent of the coefficients.
The coefficients can be ignored when finding solutions.
The solutions are always integers.
The coefficients of a linear equation directly influence the slope and intercept of the line represented by the equation.
Questions & Step-by-step Solutions
1 item
Q
Q: In the context of linear equations, which of the following statements best describes the relationship between the coefficients and the solutions of the equations?
Solution: The coefficients of a linear equation directly influence the slope and intercept of the line represented by the equation.
Steps: 7
Step 1: Understand what a linear equation is. A linear equation is an equation that makes a straight line when graphed.
Step 2: Identify the parts of a linear equation. A typical linear equation looks like this: y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Step 3: Recognize what coefficients are. In the equation y = mx + b, 'm' is the coefficient of 'x'. It tells us how steep the line is.
Step 4: Learn about the slope. The slope (m) shows how much 'y' changes for a change in 'x'. A larger slope means a steeper line.
Step 5: Understand the intercept. The y-intercept (b) is where the line crosses the y-axis. It shows the starting point of the line on the graph.
Step 6: Connect coefficients to the graph. The coefficients (m and b) determine the direction and position of the line on the graph.
Step 7: Conclude that the coefficients directly influence the slope and intercept, which in turn affects the solutions of the equation.
