An equation belongs to the same family of graphs as y=3x+5, but it has a y- intercept of 7. How could you graph the equation without finding the equation first?
To graph an equation with a specific y-intercept without finding the equation first, you need to know the slope of the line. Since the equation you provided, y = 3x + 5, has a slope of 3, we can deduce that all equations in the same family of graphs will have the same slope.
To graph an equation with a y-intercept of 7, we can use the slope-intercept form of an equation (y = mx + b), where "m" is the slope and "b" is the y-intercept. In this case, the y-intercept is given as 7.
Therefore, the equation in the same family of graphs as y = 3x + 5, but with a y-intercept of 7, can be expressed as y = 3x + 7.
To graph this equation without finding the equation first, you can start by plotting the y-intercept at (0, 7) on the coordinate plane. From there, use the slope to find additional points and then connect them to create the line. Since the slope is 3, you can visualize it as moving up 3 units vertically and 1 unit to the right.
Here's how to graph it:
1. Plot the y-intercept at (0, 7).
2. Move up 3 units on the y-axis and 1 unit to the right from the y-intercept to find another point (1, 10).
3. Repeat this process to find additional points, creating a straight line.
4. Connect all the points to form the line.
By following this method, you can graph an equation with a specific y-intercept without determining the equation itself.