To determine if two lines are parallel, you need to compare their slopes. The slope of a line can be found from its equation, which is typically in the form of either y = mx + b or Ax + By + C = 0.
1. **Find the Slope from the Equation**: If the line is given in the slope-intercept form (y = mx + b), the slope is simply m. For example, for the line y = 2x + 3, the slope is 2. For lines in standard form (Ax + By + C = 0), you can rearrange it to slope-intercept form to find the slope. For instance, from 2x + 3y – 6 = 0, you would solve for y to get y = - rac{2}{3}x + 2, giving a slope of -2/3.
2. **Compare the Slopes**: Once you have the slopes of both lines, compare them. If the slopes are equal, the lines are parallel. For example, if the two lines have slopes of 2 and 2 respectively, you would conclude that the lines are parallel. If the slopes differ, say one line has a slope of 2 and the other has a slope of 3, then the lines are not parallel.
In summary, to check if two lines are parallel, extract their slopes from their equations and see if those slopes are identical.