Final answer:
To identify another point on the line that includes (-4,-3), (20,15), and (48,36), we first calculate the slope, which is 3/4, and write the line equation. Using the line equation y = (3/4)x, we plug in x = 60 to obtain the point (60,45) on the same line.
Step-by-step explanation:
The points (-4,-3), (20,15), and (48,36) are given as points on the same line, and we are tasked with identifying another point on this same line. To find more points on the line, we can first determine the slope of the line, using the slope formula which is (change in y)/(change in x). Calculating the slope between the given points, we find that the slope is consistent and equals to (15 - (-3))/(20 - (-4)) = 18/24 = 3/4.
Knowing the slope, we can use one of the points and the slope to write the line equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Let's use the point (-4,-3) to find the y-intercept. Plugging the point into the equation, we get -3 = (3/4)(-4) + b, simplifying to -3 = -3 + b, hence b = 0. Thus, the line equation is y = (3/4)x.
To find another point on the line, we can choose any x-value and plug it into the equation to find the corresponding y-value. Let's choose x = 60 as an example. Substituting 60 for x gives us y = (3/4)(60) = 45. Therefore, the coordinates of another point on the line are (60,45).