4. in a system of equations, the first line goes through the points (4, 6) and (2, 3). the second line is…

Explanation:

Step1: Calculate slope of first line

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 6}{2 - 4} = \frac{-3}{-2} = \frac{3}{2} = 1.5$

Step2: Find equation of first line

Use point $(4,6)$: $y - 6 = 1.5(x - 4)$ Simplify: $y = 1.5x - 6 + 6$ → $y = 1.5x$

Step3: Set equations equal to solve for $x$

$1.5x = -0.75x + 6$ $1.5x + 0.75x = 6$ $2.25x = 6$ $x = \frac{6}{2.25} = \frac{6}{\frac{9}{4}} = 6 \times \frac{4}{9} = \frac{24}{9} = \frac{8}{3} \approx 2.67$ Correction: Recheck point reading: first line points are $(-4,6)$ and $(2,3)$

Step1 (Revised): Calculate correct slope

$m = \frac{3 - 6}{2 - (-4)} = \frac{-3}{6} = -0.5$

Step2 (Revised): Find correct line equation

Use point $(2,3)$: $y - 3 = -0.5(x - 2)$ Simplify: $y = -0.5x + 1 + 3$ → $y = -0.5x + 4$

Step3 (Revised): Solve for intersection $x$

Set $-0.5x + 4 = -0.75x + 6$ $-0.5x + 0.75x = 6 - 4$ $0.25x = 2$ $x = \frac{2}{0.25} = 8$

Step4: Solve for $y$ using $x=8$

$y = -0.75(8) + 6 = -6 + 6 = 0$

Answer:

D. (8, 0)