which graph shows the equation c = 10 + 3t, where c is the total cost of going to the carnival and t is the…
which graph shows the equation c = 10 + 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?
Answer
Answer:
The graph of the equation (c = 10+3t) is a straight - line with a (y) - intercept of 10 and a slope of 3. To graph it:
- Identify the (y) - intercept: When (t = 0), (c=10 + 3\times0=10). So the line crosses the (c) - axis (vertical axis) at the point ((0,10)).
- Identify the slope: The slope (m = 3=\frac{\Delta c}{\Delta t}). This means for every increase of 1 in (t), (c) increases by 3. For example, when (t = 1), (c=10 + 3\times1 = 13); when (t = 2), (c=10+3\times2=16). Plot the points ((0,10)), ((1,13)), ((2,16)) and draw a straight line through them.
Explanation:
Step1: Find the (y) - intercept
Set (t = 0) in (c = 10+3t), so (c=10).
Step2: Find the slope
The coefficient of (t) is 3, so slope (m = 3).
Step3: Plot points
Use the (y) - intercept and slope to plot points ((0,10)), ((1,13)) etc. and draw the line.