Question 5 Write an equation for a line parallel to \( -15 x+3 y=-18 \) and passing through the point \( (2,15) \) \( y=\square 99 \)

To find the equation of a line parallel to \( -15x + 3y = -18 \), you first need to rewrite it in slope-intercept form \( y = mx + b \). Rearranging gives \( 3y = 15x - 18 \) or \( y = 5x - 6 \). The slope \( m \) is 5. Since parallel lines share the same slope, your line will also have a slope of 5. Using the point-slope form, \( y - y_1 = m(x - x_1) \) with point \( (2, 15) \), you get \( y - 15 = 5(x - 2) \). Solving this yields \( y = 5x + 5 \). So, your final equation is \( y = 5x + 5 \). Did you know that parallel lines never intersect? This means they have the same slope, and you can easily imagine them as train tracks stretching off into the horizon. In our case, both lines will rise at the same rate, no matter how far you go. For real-world applications, understanding parallel lines is crucial in fields such as architecture and engineering, where precise blueprints are key. Think about designing a building or a road; you often want elements to be parallel to ensure a neat, uniform appearance, making the concepts you learn in math directly applicable to everyday projects!