Question

The line with the equation (1/2)x - (3/4)y = 6 is graphed in the xy plane. What is the x coordinate of the x-intercept of the line?

Answer 1

Given the equation:

`(1)/(2)x\text{ - }(3)/(4)y\text{ = 6}`

Let's determine the x coordinate of the x-intercept of the line.

`(1)/(2)x\text{ - }(3)/(4)y\text{ = 6 }\rightarrow\text{ }(3)/(4)y\text{ = }(1)/(2)x\text{ - 6 }\rightarrow\text{ y = (}(4)/(3))((1)/(2)x\text{ - 6)}`
`\text{ y = }(4)/(6)x\text{ - }(24)/(3)\text{ }\rightarrow\text{ y = }(2)/(3)x\text{ - 8}`

The x-intercept is therefore, at y = 0:

`\text{ 0 = }(2)/(3)x-8\rightarrow(2)/(3)x=8\text{ }`
`x\text{ = }(3)/(2)(8)\text{ }\rightarrow\text{ x = }(24)/(2)`
`\text{ x = }12`

Therefore, the x coordinate of the x-intercept of the line of the equation is 12.