Final answer:
To find the equation of the line parallel to y=-3x+8 passing through (5, 5), the same slope of -3 is used. Applying point-slope form and simplifying, the new line's equation is y=-3x+20 in slope-intercept form.
Step-by-step explanation:
The question involves writing the equation of a line in slope-intercept form that passes through a given point and is parallel to a given line. The slope-intercept form of a linear equation is expressed as y = mx + b, where m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.
To find the equation of the line passing through the point (5, 5) and parallel to y = -3x + 8, we must use the fact that parallel lines have the same slope. Therefore, the slope of the new line is also -3. Using the point-slope form which is y - y1 = m(x - x1) where (x1, y1) is a point on the line, we can substitute m = -3 and the coordinates of the given point to find b.
The equation becomes y - 5 = -3(x - 5). Simplifying this, we get y - 5 = -3x + 15. Adding 5 to both sides to solve for y, the final equation in slope-intercept form is y = -3x + 20.