find values of A and B so that the line given by Ax+By=24 has an x intercept of 6 and y-intercept of 8
To find the x-intercept, we set y to 0 and solve for x:
Ax + B(0) = 24
Ax = 24
x = 24/A
Similarly, to find the y-intercept, we set x to 0 and solve for y:
A(0) + By = 24
By = 24
y = 24/B
We know that the x-intercept is 6, so we substitute x = 6 into the equation:
6A + B(0) = 24
6A = 24
A = 4
We also know that the y-intercept is 8, so we substitute y = 8 into the equation:
A(0) + 8B = 24
8B = 24
B = 3
Therefore, A = 4 and B = 3.
To find the values of A and B such that the line given by Ax + By = 24 has an x-intercept of 6 and a y-intercept of 8, we can use the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept.
Given that the x-intercept is 6, this means that the y-coordinate is 0. Substituting these values into the equation gives us:
A * 6 + B * 0 = 24
6A = 24
A = 4
Similarly, given that the y-intercept is 8, this means that the x-coordinate is 0. Substituting these values into the equation gives us:
A * 0 + B * 8 = 24
8B = 24
B = 3
Therefore, the values of A and B that satisfy the given conditions are A = 4 and B = 3.