What is an equation of the line that is perpendicular to -x+2y=4 and passes through the point (-2, 1)

Mathematics

1 answer:

Nana76 [90]2 years ago

5 0

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

x + 2y = 4

2y = - x + 4

y = -x/2 + 4/2

y = - x/2 + 2

Comparing with the slope intercept form, slope = - 1/2

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the given line.

Therefore, the slope of the line passing through (- 2, 1) is 2

To determine the intercept, we would substitute m = 2, x = - 2 and y = 1 into y = mx + c. It becomes

1 = 2 × - 2 + c = - 4 + c

c = 1 + 4 = 5

The equation becomes

y = 2x + 5

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3 years ago

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Use the drop-down menus to complete the proof. Given that w ∥ x and y is a transversal, we know that ∠1 ≅∠5 by the . Therefore,

ololo11 [35]

Answer:

From the graph attached, we know that $\angle 1 \cong \angle 5$ by the corresponding angle theorem, this theorem is about all angles that derive form the intersection of one transversal line with a pair of parallels. Specifically, corresponding angles are those which are placed at the same side of the transversal, one interior to parallels, one exterior to parallels, like $\angle 1$ and $\angle 5$ .

We also know that, by definition of linear pair postulate, $\angle 3$ and $\angle 1$ are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.

They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that $\angle 3$ and $\angle 1$ together are 180°, because they are on a straight angle. That is, $m \angle 3 + m \angle 1 = 180\°$

If we substitute $\angle 5$ for $\angle 1$ , we have $m \angle 3 + m \angle 5 = 180\°$ , which means that $\angle 3$ and $\angle 5$ are also supplementary by definition.