a Recall that for the x-intercept the y-coordinate value is always 0. And, for the y-intercept the x-coordinate value is always 0.
B
b Recall that for the x-intercept the y-coordinate value is always 0. And, for the y-intercept the x-coordinate value is always 0.
A
a x-intercep: (24,0) y-intercep: (0,80) Graph:
Sail Area: 960 ft^2
B
b C^22AB ft^2
Practice makes perfect
a We have the linear equation 10x+3y =240. To find the intercepts, recall that the x-intercept is the x-coordinate of the point where the graphs intercepts the x-axis. When this happens the y-coordinate is always 0, therefore, we can substitute the value y=0 in our equation and solve for the corresponding x value.
We can see that the x-intercept is 24. Now we will find the y-intercept. Recall that the y-intercept is the y-coordinate of the point where the graphs intercepts the y-axis. When this happens the x-coordinate is always 0, therefore, this time we will substitute x=0 in our equation and solve for the corresponding y value.
We found that the y-intercept is 80. Knowing both intercepts, we can graph the shape of the sail. For this, we just plot the points (24,0) and (0,80). The line joining them will be our function.
Since the function gives the values in feet, we can see that the sail is a triangle with a base of 24 feet and 80 feet tall. Recall that the area of a triangle is given by A= 12bh. Let's calculate the area of the sail.
b This time we are working with the generic equation Ax + By = C. In this equation A and B cannot both be 0, and A, B, and C are positive real numbers. Just as we did in Part A, since the x-intercept the y-coordinate is always 0 we can substitute the value y=0 in our equation and solve for the corresponding x value.
Therefore, the x-intercept is given by the quotient CA. Similarly, we can find the y-intercept by substituting this time x=0, since when the y-intercept happens the x-cooordinate is always 0.
Then, the y-intercept is given by the quotient CB. In this case the triangular sail would have a base of CA ft and a height of CB ft. We can now calculate its area.
