a new line is drawn through the point (-3,6) and perpendicular to the line with x-intercept (3,0) and y intercept (0,3) . what is the equation of this new line ?

Answer:The equation of the new line is [tex]y=x+9[/tex]  or  [tex]y-6=(x+3)[/tex]Step-by-step explanation:step 1Find out the slope of the line with x-intercept (3,0) and y intercept (0,3)The formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] substitute the values[tex]m=\frac{3-0}{0-3}=-1[/tex] step 2Find the slope of the new line perpendicular to the given linewe know thatIf two lines are perpendicular,then their slopes are opposite reciprocal (the product of their slopes is equal to -1)[tex]m_1*m_2=-1[/tex]we have[tex]m_1=-1[/tex] ----> slope of the given lineso[tex]m_2=1[/tex] ---> slope of the new linestep 3Find the equation of the new line in point slope form[tex]y-y_1=m(x-x_1)[/tex]we have[tex]m=1[/tex][tex](x_1,y_1)=(-3,6)[/tex]substitute[tex]y-6=(1)(x+3)[/tex][tex]y-6=(x+3)[/tex] ----> equation in point slope formConvert to slope intercept form[tex]y=mx+b[/tex]isolate the variable y[tex]y=x+3+6[/tex][tex]y=x+9[/tex]