Question

1. write the equation of a line passing through the point (6, -4) and has an x-intercept of -2.

a $y = -2x - 4$
c $y = -\frac{1}{2}x - 1$
b $y = -2x - 1$
d $y = -\frac{1}{3}x - 4$

Explanation:

Step1: Identify two points

The line passes through \((6, -4)\) and has an \(x\)-intercept of \(-2\), so it also passes through \((-2, 0)\).

Step2: Calculate the slope

The slope \(m\) between \((x_1,y_1)=(6, -4)\) and \((x_2,y_2)=(-2, 0)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - (-4)}{-2 - 6}=\frac{4}{-8}=-\frac{1}{2}\).

Step3: Use point - slope form

Using the point - slope form \(y - y_1=m(x - x_1)\) with \((x_1,y_1)=(6, -4)\) and \(m =-\frac{1}{2}\):
\(y-(-4)=-\frac{1}{2}(x - 6)\)
\(y + 4=-\frac{1}{2}x+3\)
\(y=-\frac{1}{2}x+3 - 4\)
\(y=-\frac{1}{2}x - 1\)
We can also check by substituting \(x = 6\) into option C: \(y=-\frac{1}{2}(6)-1=-3 - 1=-4\), which matches the point \((6, -4)\). And when \(y = 0\), \(0=-\frac{1}{2}x-1\), \(\frac{1}{2}x=-1\), \(x=-2\), which matches the \(x\)-intercept.

Answer:

C. \(y =-\frac{1}{2}x - 1\)