Question

question 4
write the equation of the line that passes through the points (-4, -2) and (2, 7).
a. $y = -\frac{2}{3}x + 4$
b. $y = -\frac{3}{2}x + 4$
c. $y = \frac{3}{2}x + 4$
d. $y = \frac{2}{3}x + 4$

Explanation:

Step1: Calculate the slope

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Given points \((-4, -2)\) and \((2, 7)\), we substitute \( x_1=-4,y_1 = - 2,x_2=2,y_2 = 7 \) into the formula:
\( m=\frac{7-(-2)}{2-(-4)}=\frac{7 + 2}{2 + 4}=\frac{9}{6}=\frac{3}{2} \)

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((-4,-2)\) and \( m=\frac{3}{2} \).
Substitute into the formula: \( y-(-2)=\frac{3}{2}(x - (-4)) \)
Simplify: \( y + 2=\frac{3}{2}(x + 4) \)
Expand the right - hand side: \( y+2=\frac{3}{2}x+6 \)
Subtract 2 from both sides: \( y=\frac{3}{2}x+6 - 2=\frac{3}{2}x + 4 \)

Answer:

C. \( y=\frac{3}{2}x + 4 \)