The equation of the line with an x -intercept of 2 and a y -intercept of 4 can be written in the form y = m x + b where the number

Question

The equation of the line with an -intercept of  and a -intercept of  can be written in the form  where the number 

 is:_____

the number  is _____

Answer 1

The equation of the line with an x-intercept of 2 and a y-intercept of 4 can be written in the form y = mx + b

1. At any x-intercept in the coordinate plane, the corresponding y-value is 0
2. It can be said the line has an x-intercept at the point (2, 0)
3. At any y-intercept in the coordinate plane, the corresponding x-value is 0
4. It can be said the line has an y-intercept at the point (0, 4)
5. Knowing two distinct points in a given line enables us to calculate the slope of the line
6. Recall the Slope Formula — m = (y₂ - y₁) / (x₂ - x₁)
7. m = (4 - 0) / (0 - 2)
8. m = 4 / (-2)
9. m = -2
10. Substituting this into Slope-Intercept Form yields y = -2x + b
11. By definition of "slope-intercept," the value of b is equal to the y-coordinate of the y-intercept, so it can be determined that the resulting linear equation is y = -2x + 4
12. However if you don't know the y-intercept (unlike this particular case), the linear equation can be proven by substituting a coordinate pair along the line into the equation to solve for b as follows:
13. y = -2x + b
14. (4) = -2(0) + b
15. b = 4
16. or
17. (0) = -2(2) + b
18. b = 4
19. Therefore, the equation of the line with an x-intercept of 2 and a y-intercept of 4 can be written in the form y = -2x + 4 or y = 4 - 2x where m = -2 and b = 4

Answer 2

Since the y-intercept is 4, b = 4.

So, y = mx + 4.

Since the x-intercept is 2, 0 = 2m + 4. So, m = -2.