The correct graph for the first question is the fourth graph. The correct graph to the second question is the first graph. See the attached image for the graphical representation.
What is a straight line graph?
A straight line graph is a graph of a linear equation showing the relation between two variable. It is usually expressed in the form of a linear equation: y = mx + b
where;
- y = vertical axis (dependent variable)
- x = horizontal axis (independent variable)
- m = slope
- b = y-intercept
From the given information:
1. y is the distance left to go in a car ride after x hours of driving at a constant rate towards its destination.
The graphical illustration means that it is a straight line graph since the car is driving at a constant rate. The direction of the line graph is a downward direction since the distance of the car left to be covered will decrease as the time goes on. Thus, the correct graph is the fourth graph.
2. y is the temperature in °C, x is the temperature in, in °F.
Using the slope-intercept form of linear equation:
y = mx + b
here:
- y = temperature in °C
- x = temperature in °F
To convert Fahrenheit to Celsius, we use the general form:
It means the slope is 5/9 and the direction of the graph will be in upward-slope direction from the left to right. This means both the temperature increase with time. Thus, the first graph is the correct match.
3. y is the weight of a kitten x days after birth.
Here;
- y = weight of the kitten
- x = days of birth
The linear graph shows a constant growth such that as the kitten grows, it gain additional weight after child birth. Hence, the second graph is correct.
4. y is the amount of calories consumed eating x crackers. Using the slope-intercept equation:
y = mx + b
where;
- Slope (m) = calories consumed per cracker.
- y-intercept (b) = initial amount of calories when no crackers are eaten (i.e. when x= 0)
Thus, the third graph is correct.