Question

Find the x and y intercepts of the equation 5x - 7y = 35 using:

a. Substituting x = 0 for y-intercept and y = 0 for x-intercept
b. Factoring the equation
c. Using the quadratic formula
d. Solving for y in terms of x

Answer 1

The x and y intercepts of the equation 5x - 7y = 35 are found by setting x and y to 0 in the equation. The y-intercept is (0, -5) and the x-intercept is (7, 0). Other methods like factoring or the quadratic formula are not applicable as the equation is linear.

Step-by-step explanation:

To find the x and y intercepts of the linear equation 5x - 7y = 35, we use different methods:

1. Substituting x = 0 for y-intercept: Set x to 0 in the equation and solve for y:
   
   The y-intercept is (0, -5).
2. Substituting y = 0 for x-intercept: Set y to 0 in the equation and solve for x:
   
   The x-intercept is (7, 0).
3. Factoring: This method is not applicable as the equation is not quadratic and cannot be factored to find x and y intercepts.
4. Using the quadratic formula: This method is not relevant as the equation is linear, not quadratic.
5. Solving for y in terms of x: Rearrange the equation to solve for y:
   
   The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case, b = -5, confirming our earlier calculation for the y-intercept.