Question

If the point (3, -4) divides the intercept of a line between the coordinate axes in the ratio 2:3, then its equation is:

A. y = 2x - 3
B. 2x + 3y = 6
C. 3x + 2y = 6
D. 2x - 3y = 6

Answer 1

To find the equation of the line that passes through the point (3, -4) and divides the intercept of the line between the coordinate axes in the ratio 2:3, we can use the slope-intercept form of a linear equation, y = mx + b. By solving a system of equations, we find that the equation of the line is 2x + y = 1. The correct option is not mention.

Step-by-step explanation:

To find the equation of the line that passes through the point (3, -4) and divides the intercept of the line between the coordinate axes in the ratio 2:3, we can use the slope-intercept form of a linear equation, y = mx + b. Here's how:

1. First, let's find the coordinates of the point that divides the intercepts.
2. The x-coordinate of this point can be found using the formula: x = (2/5)(0) + (3/5)(3) = 9/5 = 1.8.
3. The y-coordinate of this point can be found using the formula: y = (2/5)(-4) + (3/5)(0) = -8/5 = -1.6.
4. Now that we have the coordinates of this point, we can use the slope-intercept form y = mx + b to find the equation of the line. Substituting the values, we get: -1.6 = m(1.8) + b.
5. Since we know that the line passes through the point (3, -4), we can substitute these values into the equation to get another equation: -4 = m(3) + b.
6. We now have a system of two equations with two variables (m and b). We can solve this system to find the values of m and b.
7. By solving the system of equations, we find that m = -2 and b = 1. The equation of the line is then y = -2x + 1, which simplifies to 2x + y = 1.

The equation of the line is 2x + y = 1. The correct option is not mention.