Is it possible to graph linear functions like h(x) = 3x + 7 without doing a table of values? If it is, how? And I know the slope is 7, which means the y-intercept is (0,7).
to graph linear functions we need 2 points
h(0)=3*0+7=7 first point (0,7)
h(1)=3*1+7=10 second point (1,10)
start with the y-intercept and plot that point.
You know the slope is 3, that is, the rise is 3 units for a run of 1, or the rise is 6 units for a run of 2 etc.
so from the y-intercept, count 3 units to the right, then 1 unit up, and mark that point.
Join the two points and you have your line.
Yes, it is possible to graph linear functions without creating a table of values. The equation you provided, h(x) = 3x + 7, can be graphed using the slope-intercept form of a linear equation, y = mx + b.
To graph a linear function using this form, you need to know the values of the slope (m) and the y-intercept (b). In this case, you mentioned that the slope is 7 and the y-intercept is (0,7).
To get the graph of the function h(x) = 3x + 7, follow these steps:
1. Start by marking the y-intercept on the graph. The y-intercept is the point (0, 7), which means that when x = 0, h(x) = 7. Plot this point on the graph.
2. Use the slope to identify another point on the line. The slope, 3 in this case, tells us how the y-coordinate changes when the x-coordinate changes. Since the slope is positive, for every 1 unit increase in x, the y-coordinate will increase by 3 units. So, starting from the y-intercept (0,7), move 1 unit to the right and then 3 units up to get another point on the line.
3. Use a straight edge or ruler to draw a line passing through the two points you plotted. Remember that a linear function represents a straight line, so it's important to extend the line beyond the points you've plotted to get a clear picture of the function.
By following these steps, you should be able to graph h(x) = 3x + 7 without having to create a table of values.