IDNLearn.com is the perfect place to get detailed and accurate answers to your questions. Join our platform to receive prompt and accurate responses from experienced professionals in various fields.

Write an equation of a line perpendicular to line CD in slope-intercept form that passes through the point [tex](-1, 6)[/tex].

A. [tex]y = -0.5x - 5.5[/tex]
B. [tex]y = -0.5x + 5.5[/tex]
C. [tex]y = 2x + 13[/tex]
D. [tex]y = 2x - 13[/tex]


Sagot :

To write the equation of a line perpendicular to line CD and passing through the point [tex]\((-1, 6)\)[/tex], we will follow these steps:

1. Determine the slope of the given line:
The equation of line CD is given as [tex]\( y = -0.5x - 5.5 \)[/tex]. Here, the slope ([tex]\(m\)[/tex]) is [tex]\(-0.5\)[/tex].

2. Find the slope of the perpendicular line:
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.

So, if the slope of line CD is [tex]\(-0.5\)[/tex], the slope ([tex]\(m_{\perpendicular}\)[/tex]) of the line perpendicular to it is:
[tex]\[ m_{\perpendicular} = -\frac{1}{-0.5} = 2 \][/tex]

3. Use the point-slope form of the line equation:
We know the slope of the perpendicular line is [tex]\(2\)[/tex] and it passes through the point [tex]\((-1, 6)\)[/tex]. The point-slope form of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Substituting [tex]\(m = 2\)[/tex], [tex]\(x_1 = -1\)[/tex], and [tex]\(y_1 = 6\)[/tex], we get:
[tex]\[ y - 6 = 2(x - (-1)) \quad \Rightarrow \quad y - 6 = 2(x + 1) \][/tex]

4. Simplify the equation to slope-intercept form:
Solve for [tex]\(y\)[/tex] to put the equation into the slope-intercept form [tex]\(y = mx + b\)[/tex]:
[tex]\[ y - 6 = 2(x + 1) \quad \Rightarrow \quad y - 6 = 2x + 2 \quad \Rightarrow \quad y = 2x + 2 + 6 \quad \Rightarrow \quad y = 2x + 8 \][/tex]

Hence, the equation of the line in slope-intercept form is:
[tex]\[ y = 2x + 8 \][/tex]

Thus, among the given choices, the equation that matches this is not provided directly. Correcting the choice, the final correct answer is:
[tex]\( y = 2x + 8 \)[/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.