Question

write an equation of the line that passes through a pair of points: (-4, -3), (-3, 1)
a. y = 4x - 13
b. y = -4x + 13
c. y = 4x + 13
d. y = 4x - \frac{1}{13}
please select the best answer from the choices provided
\bigcirc a
\bigcirc b
\bigcirc c
\bigcirc d

Explanation:

Step1: Calculate the slope

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

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 \((-3,1)\) (we could also use \((-4,-3)\)). Substituting \( m = 4 \), \( x_1=-3 \), and \( y_1 = 1 \) into the point - slope form, we get \( y-1 = 4(x-(-3)) \), which simplifies to \( y - 1=4(x + 3) \).

Step3: Simplify the equation

Expand the right - hand side: \( y-1=4x+12 \). Then add 1 to both sides to get \( y=4x + 13 \). We can also check by substituting the points into the equation. For \((-4,-3)\): Left - hand side \( y=-3 \), Right - hand side \( 4\times(-4)+13=-16 + 13=-3 \). For \((-3,1)\): Left - hand side \( y = 1 \), Right - hand side \( 4\times(-3)+13=-12 + 13 = 1 \).

Answer:

C. \( y = 4x+13 \)