The coefficient in front of the variable x gives the slope. The first two have a slope of 5, but different y intercepts. They're parallel to each other. The third and fourth both have a slope of 1 and are less steep than the first two. They have different y intercepts and are also parallel to each other.
To determine the slopes and parallelism of the given equations, we can observe their standard form, which is: y = mx + b. In this form, the coefficient in front of the variable x, represented by m, gives us the slope of the line.
First Two Equations:
The first two equations have a slope of 5, which means their respective lines go up or down by 5 units for every 1 unit moved horizontally. Since they have different y-intercepts (represented by b), they are parallel but located at different positions on the y-axis.
Third and Fourth Equations:
The third and fourth equations have a slope of 1, indicating that their lines go up or down by 1 unit for every 1 unit moved horizontally. Since they also have different y-intercepts, they are parallel to each other. However, compared to the first two equations, these lines are less steep because their slope is smaller.
In summary:
1. The first two equations have a slope of 5, are parallel, and have different y-intercepts.
2. The third and fourth equations have a slope of 1, are parallel, and also have different y-intercepts.
3. The first two equations are steeper since their slope is larger, whereas the third and fourth equations are less steep due to their smaller slope.