Question

Верно ли данное утверждение? Если угловые коэффициенты прямых, являющихся графиками двух линейных функций, различны, то эти прямые не пересекаются, а если угловые коэффициенты одинаковы, то прямые параллельны.

Answer 1

Графики двух линейных функций, заданных формулами вида y = аx+b, пересекаются, если коэффициенты при х различны, и параллельны, если коэффициенты при х одинаковы. То есть, утверждение верно.

Answer 2

Verifying the Claim

The claim states that if the slopes (or angular coefficients) of the lines, which are graphs of two linear functions, are different, then the lines do not intersect. It also states that if the slopes are the same, then the lines are parallel.

Answer

The given statement is correct. If the slopes of two lines are different, then the lines do not intersect, and if the slopes are the same, then the lines are parallel.

This can be explained using the fact that the slope of a line represents the rate of change of the line. If two lines have different slopes, it means they have different rates of change and therefore will not intersect. Conversely, if the slopes are the same, the lines have the same rate of change and will never intersect, making them parallel.

In summary: - If the slopes are different, the lines do not intersect. - If the slopes are the same, the lines are parallel.