Question

question 12 (1 point)
what is an equation of the line?

a ( y + 3 = -(x - 2) )
b ( y + 1 = 2(x + 2) )
c ( y + 3 = (x + 2) )
d ( y - 3 = 2(x - 2) )

Explanation:

Step1: Find the slope

We can use two points, say \((-2, -3)\) and \((2, 1)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1 - (-3)}{2 - (-2)}=\frac{4}{4} = 1\).

Step2: Use point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Let's use the point \((-2,-3)\), then \(y-(-3)=1\times(x - (-2))\), which simplifies to \(y + 3=(x + 2)\). We can also check other points. For example, using the point \((2,1)\): \(y-1 = 1\times(x - 2)\), \(y-1=x - 2\), \(y=x - 1\). If we substitute \(x=-2\) into \(y=x - 1\), we get \(y=-3\), which matches the point \((-2,-3)\). Now let's check the options:

• Option a: \(y + 3=-(x - 2)\) has slope \(- 1\), incorrect.
• Option b: \(y + 1=2(x + 2)\) has slope \(2\), incorrect.
• Option c: \(y + 3=(x + 2)\) has slope \(1\) and passes through \((-2,-3)\), correct.
• Option d: \(y - 3=2(x - 2)\) has slope \(2\), incorrect.

Answer:

c. \(y + 3=(x + 2)\)