Answer:
Explanation:
The relations between straight lines and linear equations are closely connected. In fact, every straight line can be represented by a linear equation, and every linear equation represents a straight line.
A linear equation has the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). The slope represents the rate of change of the line, while the y-intercept represents its starting point.
For example, let's say we have the linear equation y = 2x + 3. The slope of this line is 2, which means that for every 1 unit increase in x, y will increase by 2 units. The y-intercept is 3, which means that the line starts at the point (0, 3) on the y-axis.
Conversely, if we have a straight line in the coordinate plane, we can find its corresponding linear equation by using the slope-intercept form. First, we determine the slope of the line by selecting any two points on the line and finding the ratio of the change in y to the change in x. Then, we can substitute one of the points and the slope into the equation y = mx + b to find the value of b.
For example, if we have a line passing through the points (2, 4) and (5, 10), we can calculate the slope as (10 - 4) / (5 - 2) = 2. Using the point (2, 4) and the slope of 2, we can substitute these values into the equation y = mx + b to find that b = 0. Therefore, the linear equation representing this line is y = 2x.
In summary, straight lines and linear equations are related in that every straight line can be represented by a linear equation, and every linear equation represents a straight line. The slope of the line represents its rate of change, and the y-intercept represents its starting point. By understanding these concepts, we can easily describe and analyze the relations between straight lines and linear equations.