Find the x and y Intercept of 9x+5y=4

## Find the x-intercept of the line 6x+2y=12

# 2 Answers

(x,0) are coordinates of x-intercept.

(0,y) are coordinates of y-intercept

~~~~~~~~~~~

**1.** 6x + 2 · 0 = 12 ---> 6x = 12 ---> x = 2

So, the x-intercept is **(2 , 0)**

6 · 0 + 2y = 12 ---> 2y = 12 ---> y = 6 .

the y-intercept is** (0 , 6)**

**2.** 9x + 5 · 0 = 4 ---> 9x = 4 ---> x = 4/9 ; **(4/9 , 0)**

9 · 0 + 5y = 4 ---> 5y = 4 ---> y = 4/5 ; **(0 , 4/5)**

Rearrange the equation of the line into slope-intercept form: y = mx + b ,

where m is the slope of the line and b is the y-intercept (the y-intercept is the point where x= 0).

6x + 2y = 12 subtract 6x from both sides of the equation

2y = -6x + 12 divide both sides of the equation by 2

**y = -3x + 6** ==> **y-intercept** (**b**):
**y = 6**

Conversely, the x-intercept is the point where y = 0:

y = -3x + 6

0 = -3x + 6 add 3x to both sides of the equation

3x = 6 divide both sides of the equation by 3

**x = 2** ==> **x-intercept**

The slope-intercept form of the line given by the equation 9x + 5y = 4 is as follows:

5y = -9x + 4 after subtracting 9x from both sides of the equation, divide both sides by 5

**y = (-9/5)x + (4/5)**

The **y-intercept** here is given by b; thus, **y = 4/5**.

Solving for x when y = 0 yields the x-intercept:

0 = (-9/5)x + (4/5)

(9/5)x = (4/5)

(5/9)(9/5)x = (4/5)(5/9)

**x = 4/9** ==> **x-intercept **