how do you change a linear equation to make the graph steeper?
To make the graph of a linear equation steeper, you need to change the slope of the line. The slope determines how steep or flat the line appears. Here's how you can change the slope to make the graph steeper:
1. Recall that the equation of a line can be written in the form y = mx + b, where m represents the slope.
2. To make the graph steeper, increase the slope value (m). Factors such as 2, 3, -2, -3, etc., will make the line steeper because they determine how much the x-values change for every 1 unit change in y.
3. For example, if you have the equation y = 2x + 4, increasing the slope to y = 4x + 4 will make the graph steeper. Similarly, changing the slope to y = -2x + 4 will also make the graph steeper, but in the opposite direction.
4. On the contrary, decreasing the slope value, such as y = 0.5x + 4 or y = -0.5x + 4, will make the line less steep.
Remember, changing the slope value only affects how steep the line appears. The y-intercept (b) does not affect the steepness but shifts the line up or down along the y-axis.