Find an equation for the line which passes through (-1,3) and is perpendicular to the line containing (0,3) and (4,7). The equation of the line is . (Simplify your answer. Type your answer in slope-intercept form.)

Answer:Equation of the line is y = -x + 4Step-by-step explanation:When the two lines having their slopes [tex]m_{1}[/tex] and [tex]m_{2}[/tex] are perpendicular to each other then [tex]m_{1}\times m_{2}=-1[/tex]If [tex]m_{1}[/tex] is the slope of the line passing through two points (0, 3) and (4, 7) then [tex]m_{1}=\frac{y-y'}{x-x'}[/tex]= [tex]\frac{7-3}{4-0}[/tex]= 1Now slope of the second line perpendicular to first line will be [tex]m_{2}[/tex] = [tex]-\frac{1}{m_{2} }[/tex][tex]m_{2}[/tex] = -1Slope intercept form of the equation of a line is represented by y = mx + cwhere m = slope c = y interceptSince the line is passing through (-1, 3) and slope = -1, therefore,3 = -1 + cc = 4Now we plug in these values in the equation.y = -x + 4Equation of the line is y = -x + 4