Final answer:
One line has a positive slope and the other has a negative slope. They have the same steepness and slant in opposite directions. The lines cross at the origin.
Step-by-step explanation:
When we talk about the slope of a line and its characteristics, we are dealing with the concepts of steepness and direction, which are fundamental in the study of graphs in algebra. In the given question, one line has a positive slope while the other has a negative slope. This means that their steepness, while it may be the same numerically, will appear different visually because they slant in opposite directions. The line with the positive slope climbs upward as you move to the right on the graph, while the line with the negative slope goes down as you move to the right. If two lines have slopes with different signs (one positive, one negative) but the same absolute value, they are said to have the same steepness but slope in opposite directions. If the lines cross at the origin, it means that they intersect at the point (0, 0) on a graph. Knowing this, we can fill in the blanks as follows:
- has negative
- the same
- opposite
- cross
A straight line's slope remains constant along its entire length, as seen in Figure A1. Furthermore, a higher positive or negative value for a slope indicates a steeper line. Algebra helps us understand how the equation of a line, specifically the b and m terms, determines its shape—'b' being the y-intercept and 'm' being the slope.