what is the equation of a line with a y-intercept of 6 and an x-intercept of 9

Answer 1

What is the equation of a line with a y-intercept of 6 and an x-intercept of 9?

1. If the line has a y-intercept at 6, then the line passes through the point (0, 6)
2. If the line has an x-intercept at 9, then the line passes through the point (9, 0)
3. Knowing two points on a line, we can calculate the slope and resultantly find the equation of the line
4. Recall the slope formula - m = (y₂ - y₁) / (x₂ - x₁)
5. Let (9, 0) = (x₁, y₁) and (0, 6) = (x₂, y₂)
6. m = (6 - 0) / (0 - 9) = 6 / (-9) = -2/3
7. Recall the point-slope form of a line, derived from the slope formula - (y - y₁) = m(x - x₁)
8. Let either (9, 0) or (0, 6) equal (x₁, y₁)
9. Substitute values of m, x₁, and y₁ into the point-slope form linear equation and simplify
10. (y - 6) = (-2/3)(x - 0)
11. y - 6 = (-2/3)x
12. y = (-2/3)x + 6

Therefore, the equation of a line with a y-intercept of 6 and an x-intercept of 9 is y = (-2/3)x + 6