What is the slope and y intercept for the multiples of 3

To find the slope and y-intercept for the multiples of 3, we need to express these multiples in a linear equation form, such as y = mx + b, where m is the slope and b is the y-intercept.

The multiples of 3 can be represented by a line that passes through all points (x, y) where y is a multiple of 3. This means the equation will look like y = 3x. In this equation:

- The coefficient of x (which is 3) represents the slope (m). So, the slope is 3. - Since there is no constant term added or subtracted from 3x, the y-intercept (b) is 0.

Therefore, the slope is 3, and the y-intercept is 0 for the line that represents the multiples of 3.

Extra: The concept of slope and y-intercept are fundamental in understanding linear equations and graphing lines.

Slope (m) - The slope tells us how steep a line is or the rate at which y increases as x increases. The slope is calculated by the change in y over the change in x between any two points on the line (often referred to as "rise over run"). A positive slope means the line is going upwards when moving from left to right, while a negative slope means the line is going downwards.

Y-intercept (b) - The y-intercept is the point where the line crosses the y-axis. This is the value of y when x is zero. On a graph, this can be seen as the point at which the line would "intersect" the vertical y-axis.

In our case, the line representing the multiples of 3 has a slope of 3, meaning that for every one unit increase in the x-value, the y-value increases by three units. Since the y-intercept is 0, it tells us that the line crosses the y-axis at the origin (0,0). Every point on this line will have a y-value that is a multiple of 3. This line's equation doesn't include a constant term, so the line passes through the origin, and the y-value is zero when x is zero.