Question

which equation describes this line?
(1, 13)
10
(-2, 4)
-10
10
-10
a. $y - 4 = 3(x - 2)$
b. $y - 2 = 3(x - 4)$
c. $y - 4 = 3(x + 2)$
d. $y - 1 = 3(x - 13)$

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((-2, 4)\) and \((1, 13)\), we have \( m=\frac{13 - 4}{1 - (-2)}=\frac{9}{3} = 3\).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope. We can use the point \((-2,4)\). Substituting \(x_1=-2\), \(y_1 = 4\) and \(m = 3\) into the point - slope form, we get \(y-4=3(x - (-2))\), which simplifies to \(y - 4=3(x + 2)\). We can also check with the point \((1,13)\). Substituting \(x_1 = 1\), \(y_1=13\) and \(m = 3\) into the point - slope form, we get \(y-13=3(x - 1)\), but this is not one of the options. The option C uses the point \((-2,4)\) correctly in the point - slope form.

Answer:

C. \(y - 4=3(x + 2)\)