Final answer:
To find the equation in slope-intercept form that is parallel to y=3-5x and goes through the point (9,2), we use the slope-intercept form and the point-slope form to find the equation. The resulting equation is y=-5x+47.
Step-by-step explanation:
To find an equation in slope-intercept form that is parallel to y=3-5x and goes through the point (9,2), we need to consider that parallel lines have the same slope. The slope-intercept form of an equation is y=mx+b, where m is the slope and b is the y-intercept.
Given that the equation y=3-5x has a slope of -5, the parallel equation will also have a slope of -5. Using the point-slope form, we can plug in the values to find the equation: y-y1 = m(x-x1).
Substituting the values x1=9, y1=2, and m=-5, we get y-2 = -5(x-9). Simplifying gives us the equation of the parallel line: y=-5x+47.
Learn more about Slope-intercept form of equations