Final answer:
The equation of a line that contains the point (6,4) and is parallel to another line can be found by using the slope, which will be the same for parallel lines, and calculating the y-intercept based on the given point. For instance, if the slope is 3, the equation would be y = 3x - 14.
Step-by-step explanation:
To determine the equation of a line that contains the point (6,4) and is parallel to another line, we must understand two critical components of a linear equation: the slope (represented by m) and the y-intercept (represented by b). The slope is defined as the rise over the run, indicating how much the line moves up or down for each unit of horizontal movement (run). Two lines are parallel if they have the same slope.
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Since we want a line parallel to another, we will keep the same slope, and our task is to find the y-intercept that allows the line to pass through the point (6,4).
To find the y-intercept, we rearrange the formula to b = y - mx and substitute the coordinates of the point (6,4) into the equation, assuming we know the slope (m).
For example, if the slope of the original line is 3, our new equation would also have a slope of 3, therefore, we would calculate the y-intercept as follows:
- b = 4 - (3)(6)
- b = 4 - 18
- b = -14
Hence, the equation of our new line is y = 3x - 14.