Get the answers you've been searching for with IDNLearn.com. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

Choose the equation below that represents the line passing through the point [tex][tex]$(-5, 1)$[/tex][/tex] with a slope of [tex]\frac{3}{2}[/tex].

A. [tex]y - 5 = \frac{3}{2}(x + 1)[/tex]

B. [tex]y + 1 = \frac{3}{2}(x - 5)[/tex]

C. [tex]y + 5 = \frac{3}{2}(x - 1)[/tex]

D. [tex]y - 1 = \frac{3}{2}(x + 5)[/tex]


Sagot :

To find the equation of the line passing through the point [tex]\((-5, 1)\)[/tex] with a slope of [tex]\(\frac{3}{2}\)[/tex], we can use the point-slope form of the equation of a line. The point-slope form is given by:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope of the line. In this problem, the point [tex]\((-5, 1)\)[/tex] is given along with the slope [tex]\(m = \frac{3}{2}\)[/tex].

Plugging in the given point and slope into the point-slope form equation, we have:

[tex]\[ y - 1 = \frac{3}{2}(x - (-5)) \][/tex]

Since subtracting a negative number is equivalent to adding the positive counterpart, we can simplify the equation:

[tex]\[ y - 1 = \frac{3}{2}(x + 5) \][/tex]

Therefore, the correct equation of the line is:

[tex]\[ y - 1 = \frac{3}{2}(x + 5) \][/tex]

Comparing this with the options provided:

1. [tex]\(y - 5 = \frac{3}{2}(x + 1)\)[/tex]
2. [tex]\(y + 1 = \frac{3}{2}(x - 5)\)[/tex]
3. [tex]\(y + 5 = \frac{3}{2}(x - 1)\)[/tex]
4. [tex]\(y - 1 = \frac{3}{2}(x + 5)\)[/tex]

We see that option 4 matches our derived equation. Hence, the correct choice is:

[tex]\[ \boxed{y - 1 = \frac{3}{2}(x + 5)} \][/tex]