Question

The inequality of the graph

Answer 1

`\displaystyle y > 4x - 2`

Explanation:

Starting from the y-intercept of
`\displaystyle [0, -2],`you do
`\displaystyle (rise)/(run)`by either moving four blocks south over one block west or four blocks north over one block east [west and south are negatives]. Next, we have to determine the types of inequality symbols that are suitable for this graph, which will be less than and greater than since this is a dashed line graph. We then use the zero-interval test [test point (0, 0)] to ensure whether we shade the opposite portion [portion that does not contain the origin] or the portion that DOES contain the origin. At this step, we must verify the inequalities as false or true:

Greater than

`\displaystyle 0 > 4[0] - 2 → 0 > -2`☑

Less than

`\displaystyle 0 < 4[0] - 2 → 0 ≮ -2`

This graph is shaded in the portion of the origin, so you would choose the greater than inequality symbol to get this inequality:

`\displaystyle y > 4x - 2`

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