In the table, we have four ordered pairs of x-values and y-values. Let's plot them as points on the coordinate plane and draw a line through them.
Looking at the graph, we see that the line crosses the y-axis at (0,3). This means that the y-intercept is 3. Next, we will use two of the points to find the slope. Let's use ( 8, 15) and ( 6, 12).
change in y/change in x = m
⇓
15- 12/8- 6= 3/2
Now we can write a linear equation in slope-intercept form that relates y to x.
y= 3/2x+ 3
The slope of a linear equation describes the ratio of change between x and y. The y-intercept indicates the value of x when y is 0. Let's interpret what this means for our equation, where x is the age (in months) and y is the weight (in pounds) of a puppy.
y=3/2x+ 3
In this case the slope indicates that every 2 weeks the puppy gains 3 pounds in weight. The y-intercept indicates that a newborn puppy weighs 3 pounds.
We want to calculate after how many weeks the puppy will weigh 33 pounds. In other words, we want to know for what value of x will y be equal to 33. To do this, we will substitute y= 33 into our linear equation from Part B and solve for x. Remember to follow the Properties of Equality when solving an equation.
