Write an equation of the line that passes through the given point and is parallel to the given line.40. (4,1);y=-2x+7 41. (0,6);y=5x-3 42. (-5,-2);y=2/3x+1

Answer:Part 40) [tex]y=-2x+9[/tex]Part 41) [tex]y=5x+6[/tex]Part 42) [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]Step-by-step explanation:Remember that If two lines are parallel, then their slopes are the samePart 40) Write an equation of the line that passes through the given point and is parallel to the given linewe havePoint (4,1)Given line y=-2x+7step 1Find the slope of the given lineThe given line is a equation of the line in slope intercept form[tex]y=mx+b[/tex]wherem is the slope b is the y-interceptsoThe slope of the given line is[tex]m=-2[/tex]step 2Find the y-intercept bwe have[tex]m=-2[/tex] [tex](4,1)[/tex]substitute in the linear equation[tex]1=(-2)4+b[/tex]solve for b[tex]b=1+8[/tex][tex]b=9[/tex]step 3Find equation of the line that passes through the given point and is parallel to the given linewe have[tex]m=-2[/tex] [tex]b=9[/tex]substitute The equation of the line is[tex]y=-2x+9[/tex]Part 41) Write an equation of the line that passes through the given point and is parallel to the given linewe havePoint (0,6)Given line y=5x-3step 1Find the slope of the given lineThe given line is a equation of the line in slope intercept form[tex]y=mx+b[/tex]wherem is the slope b is the y-interceptsoThe slope of the given line is[tex]m=5[/tex]step 2Find the y-intercept b[tex]b=6[/tex] ----> because the y-intercept is the point (0,6) (value of y when the value of x is equal to zero)step 3Find equation of the line that passes through the given point and is parallel to the given linewe have[tex]m=5[/tex] [tex]b=6[/tex] substitute in the linear equation[tex]y=5x+6[/tex]Part 42) Write an equation of the line that passes through the given point and is parallel to the given linewe havePoint (-5,-2)Given line y=(2/3)x+1step 1Find the slope of the given lineThe given line is a equation of the line in slope intercept form[tex]y=mx+b[/tex]wherem is the slope b is the y-interceptsoThe slope of the given line is[tex]m=\frac{2}{3}[/tex]step 2Find the y-intercept bwe have[tex]m=\frac{2}{3}[/tex][tex](-5,-2)[/tex]substitute in the linear equation[tex]-2=(\frac{2}{3})(-5)+b[/tex]solve for b[tex]-2=-\frac{10}{3}+b[/tex][tex]b=-2+\frac{10}{3}[/tex][tex]b=\frac{4}{3}[/tex]step 3Find equation of the line that passes through the given point and is parallel to the given linewe have[tex]m=\frac{2}{3}[/tex][tex]b=\frac{4}{3}[/tex]substitute The equation of the line is[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]