What is the equation in slope-intercept form of a line that is perpendicular to y=2x+2 and passes through the point (4, 3)?
1 answer:
<h2>Answer: y = - ¹/₂ x + 5
</h2><h3>Step-by-step explanation:
</h3>
<u>Find the slope of the perpendicular line</u>
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.
⇒ if the slope of this line = 2 (y = 2x + 2)
then the slope of the perpendicular line (m) = - ¹/₂
<u>Determine the equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 3 = - ¹/₂ (x - 4)
We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:
since y - 3 = - ¹/₂ (x - 4)
y = - ¹/₂ x + 5 (in slope-intercept form)
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Second option: On a coordinate plane, rectangle A'B'C'D' prime has points
(See the graph attached)
Step-by-step explanation:
For this exercise it is importnat to know that a Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) has the same shape as the Pre-Image (which is the original figure before the transformation), but they have different sizes.
In this case, you know that the vertices of the rectangle ABCD ( The Pre-Image) are the following:
Therefore, to find the vertices of the rectangle A'B'C'D' (The Image) that results of dilating the rectangle ABCD by a factor of 4 about the origin, you need to multiply the coordinates of each original vertex by 4. Then, you get:
Finally, knowing those points, you can identify that the graph that shows the result of that Dilation, is the one attached.
