Question

Which line represents “a number is one-half the difference of a number x and 4?”

Answer 1

Line C

Explanation:

Given:

• "a number y is one-half the difference of a number x and 4”.

Create the equation for the line using the given information:

`\implies y=(1)/(2)(x-4)`

Distribute:

`\implies y=(1)/(2)x-2`

`\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}`

Compare the found equation with the slope-intercept formula:

• Slope = ¹/₂
• y-intercept = -2

The y-intercept is the y-value of the point at which the line crosses the y-axis. Therefore, the line crosses the y-axis at y = -2.

The slope tells us how much y increases as x increases. Given the slope is ¹/₂, the line increases by one y-value for every two x-values.

Therefore, the line that represents the given information is line C.