Question 701278
first find the equation of  the line passing through the points ({{{-2}}}, {{{-3}}}) and ({{{2}}},{{{5}}})

*[invoke find_equation_of_line -2, -3, 2, 5]


since we are looking for the equation of the line that passes through the point ({{{-1}}},{{{3}}}) and is parallel to the line {{{y=2x+1}}}, we will find it using given point and a slope of {{{y=2x+1}}} which is {{{m=2}}} because parallel lines have same slope

*[invoke find_line_by_slope_and_point -1, 3, 2]

so, we found that the lines {{{y=2x+1}}} and {{{y=2x+5}}} are parallel lines, that the line {{{y=2x+1}}} passing through the points ({{{-2}}}, {{{-3}}}) and ({{{2}}},{{{5}}}), and the line {{{y=2x+5}}} passing through the point ({{{-1}}},{{{3}}})

see it all on a graph:

{{{drawing(600,600,-10,10,-10,10,grid(1),circle(-2,-3,0.2),circle(2,5,0.2),circle(-1,3,0.2),graph(600,600,-10,10,-10,10,2x+5,2x+1))}}}