the graph of a line in the xy-plane has slope of 7 and contains the point(6,28). A second line passes through the points (3,7) and (-1,-13). These lines intersect at point (x,y). What is the value of x?

Answer:x = 3Step-by-step explanation:We require the equations of the 2 lines.The equation of a line in slope- intercept form isy = mx + c ( m is the slope and c the y- intercept )The line has slope = 7, hencey = 7x + c ← is the partial equationTo find c substitute (6, 28) into the partial equation28 = 42 + c ⇒ c = 28 - 42 = - 14y = 7x - 14 → (1)Calculate the slope of the second line using the slope formulam = (y₂ - y₁ ) / (x₂ - x₁ )with (x₁, y₁ ) = (3, 7) and (x₂, y₂ ) = (- 1, - 13)m = [tex]\frac{-13-7}{- 1-3}[/tex] = [tex]\frac{-20}{-4}[/tex] = 5, thusy = 5x + c ← is the partial equationTo find c substitute either of the 2 points into the partial equationUsing (3, 7), then7 = 15 + c ⇒ c = 7 - 15 = - 8y = 5x - 8 → (2)Solving (1) and (2) by equating the right sides7x - 14 = 5x - 8 ( subtract 5x from both sides )2x - 14 = - 8 ( add 14 to both sides )2x = 6 ( divide both sides by 2 )x = 3The x- coordinate of the point of intersection is x = 3