Question

find the slope and y-intercept of the line through the point (7,6) that cuts off the least area from the first quadrant.

Answer 1

To find the slope and y-intercept of the line through the point (7,6) that cuts off the least area from the first quadrant, we can use the equation y = mx + b. The slope can be found using the formula (y2 - y1) / (x2 - x1), and the y-intercept can be found by substituting the slope and a point into the equation.

Step-by-step explanation:

To find the slope and y-intercept of the line through the point (7,6) that cuts off the least area from the first quadrant, we can use the equation y = mx + b, where m represents the slope and b represents the y-intercept.

Given that we want to find the line that cuts off the least area, we need to find the line that is closest to the origin. This means that the line must pass through the point (0,0).

Using the points (7,6) and (0,0), we can find the slope:

slope = (y2 - y1) / (x2 - x1) = (0 - 6) / (0 - 7) = -6 / -7 = 6/7

Next, we can substitute the slope and the point (7,6) into the equation y = mx + b to find the y-intercept:

6 = (6/7)(7) + b

6 = 6 + b

b = 0

Therefore, the equation of the line is y = (6/7)x.

Answer 2

The slope of the line is 6/7 and the y-intercept is 0.

Step-by-step explanation:

Given point = (7,6)

To find the slope and y-intercept of the line through the point (7,6) that cuts off the least area from the first quadrant, we can use the equation y = mx + b.

The slope can be found using the equation m = (y2 - y1) / (x2 - x1).

Substituting the values (7,6) and (0,0) into the equation, we get m = (6 - 0) / (7 - 0) = 6/7.

The y-intercept can be found using the equation b = y - mx.

Substituting the values (7,6) and m = 6/7 into the equation, we get b = 6 - (6/7) * 7 = 6 - 6 = 0.