Math  /  Algebra

Question4. \perp pr. wnich equation represents the line in point-slope form that passes through (3,5)(-3,5) and has a slope of 12-\frac{1}{2}. A. y5=12(x+3)y-5=\frac{1}{2}(x+3) B. y+5=12(x3)y+5=-\frac{1}{2}(x-3) C. y5=12(x+3)y-5=-\frac{1}{2}(x+3) D. y+5=12(x3)y+5=\frac{1}{2}(x-3)

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that goes through the point (3,5)(-3, 5) and has a slope of 12-\frac{1}{2}, and we want that equation in point-slope form. Watch out! Don't mix up the signs of the coordinates when plugging them into the point-slope form!
Also, remember point-slope form is yy1=m(xx1)y - y_1 = m(x - x_1), not y+y1y + y_1 or anything like that!

STEP 2

1. Write down the point-slope form.
2. Plug in the given point and slope.
3. Simplify (if necessary).
4. Compare to the choices.

STEP 3

Let's **kick things off** with the **point-slope form** of a linear equation, which is yy1=m(xx1)y - y_1 = m(x - x_1).
Here, mm is the **slope**, and (x1,y1)(x_1, y_1) is a **point** on the line.
This form is **super useful** because it makes it easy to write the equation of a line when you know a point and the slope.

STEP 4

We're given the point (3,5)(-3, 5), so x1=3x_1 = -3 and y1=5y_1 = 5.
Our slope is m=12m = -\frac{1}{2}.
Let's **plug these values** into our **point-slope form**: y5=12(x(3))y - 5 = -\frac{1}{2}(x - (-3)).

STEP 5

We can **simplify** the expression inside the parentheses: x(3)x - (-3) becomes x+3x + 3.
So, our equation becomes y5=12(x+3)y - 5 = -\frac{1}{2}(x + 3).

STEP 6

Now, let's **compare** our equation y5=12(x+3)y - 5 = -\frac{1}{2}(x + 3) to the answer choices.
Looks like **choice C** is a **perfect match**!

STEP 7

The equation of the line in point-slope form is y5=12(x+3)y - 5 = -\frac{1}{2}(x + 3), which is **choice C**.

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