write an equation in slop-intercept form for the line that passes through (-3,1) and is parallel to y=2x-4

Answer:The equation of line in slop-intercept form is given by:[tex]y=2x+7[/tex]Step-by-step explanation:Given equation of line:[tex]y=2x-4[/tex]To find the equation of line parallel to the line of the given equation and passes through point (-3,1).Applying slope relationship between perpendicular lines.[tex]m_1=m_2[/tex]where [tex]m_1[/tex] and [tex]m_2[/tex] are slopes of parallel lines.For the given equation in the form [tex]y=mx+b[/tex] the slope [tex]m_2[/tex] can be found by comparing [tex]y=2x-4[/tex] with standard form.∴ [tex]m_2=2[/tex]Thus slope of line parallel to this line [tex]m_1[/tex] would be given as:∴ [tex]m_1=2[/tex]The line passes through point (-3,1)Using point slope form:[tex]y-y_1=m(x-x_1)[/tex]Where [tex](x_1,y_1)\rightarrow (-3,1)[/tex] and [tex]m=m_2=2[/tex]So,[tex]y-1=2(x-(-3))[/tex][tex]y-1=2(x+3)[/tex]Using distribution.[tex]y-1=(2\times x)+(2\times 3)[/tex][tex]y-1=2x+6[/tex]Adding 1 to both sides.[tex]y-1+1=2x+6+1[/tex][tex]y=2x+7[/tex]Thus the equation of line in slop-intercept form is given by:[tex]y=2x+7[/tex]