The slope of the line through the points (12, 14) and (42, 49) is 7/6. To graph the line, start at the origin and plot points by moving 7 units up for every 6 units to the right, indicating a consistent proportional relationship.
To graph the line using the slope, we can start from one of the points, and then use the slope to find another point. Taking the point (12, 14) as the starting point, we can use the slope of 7/6 to find the next point. Since the slope represents the ratio of the change in y-coordinates to the change in x-coordinates, we can go up 7 units and right 6 units from the starting point to find the next point. Plotting these two points on a graph and connecting them with a straight line will give us the graph of the line.
To find the slope of the line passing through the points (12, 14) and (42, 49), we use the formula for slope:
slope (m) = (y2 - y1) / (x2 - x1)
Here, (x1, y1) = (12, 14) and (x2, y2) = (42, 49).
Plugging in the values:
slope (m) = (49 - 14) / (42 - 12) = 35 / 30 = 7 / 6
This means there is a rise of 7 units for every horizontal increase of 6 units, and since the relationship is proportional, the line will pass through the origin (0,0).
To graph this line, start at the origin, and using a scale, move 7 units up for every 6 units to the right. Repeating this process will give you enough points to draw the proportional relationship.