find an equation of the line that pases (8,17) and is perpendicular to the line x+2y=2

Answer:y = 2x + 1Step-by-step explanation:The equation of line is given in this format:y = mx + bWhere m is the slope and b is the y-interceptNow, let's take this equation and put it in this format:[tex]x+2y=2\\2y=-x+2\\y=-\frac{1}{2}x+1[/tex]Line perpendicular to this will have slope that is "negative reciprocal" of this. Which means that it will be "flipped" and negative of this line's slope.The slope of this line is [tex]-\frac{1}{2}[/tex]  and thus perpendicular line has slope 2So perpendicular line will have equation:y = mx + by = 2x + bPasses through the point (8,17), so we plug in x = 8 and y = 17 and get b:[tex]y = 2x + b\\17=2(8)+b\\17=16+b\\b=17-16\\b=1[/tex]So, the equation is:y = 2x + 1