Question

Write the equation of the line passing through the points (-7,9) and (7,3).

The equation of the line is
(Type your answer in slope-irnercept form. Use integers or fractions for any numbers

Answer 1

`y = -(3)/(7)x + 6`

Explanation:

1. The slope-intercept form of any linear equation is y = mx + b, where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept.

2. To find the slope from the two points (-7,9) and (7,3), we can use the formula
`(y_2-y_1)/(x_2-x_1)` and plug their values into the corresponding variable.

• 
  `(3-9)/(7-(-7))`
• 
  `(-6)/(14)`
• 
  `-(3)/(7)`

3. Okay, great! We have our slope, so our equation should look like this so far:
`y = -(3)/(7)x + b`

4. To find b, the y-intercept, we can use the equation
`b = y_1 - m * x_1` and then plug in the values to their corresponding variable.

• 
  `b = 9 - (-(3)/(7)) * (-7)`

• 
  `b = 9 - (21)/(7)`
• 
  `b = 9 - 3`
• 
  `b = 6`

5. Now that we have our slope (-3/7) and y-intercept (6), we can plug in those values into m and b and get the equation:
`y = -(3)/(7)x + 6`