Which equation represents a line that passes through (5, 1) and has a slope of 1/2 ?y-5= {1/2(x-1)y-1/2 = 5(x-1)y-1=1/2(x-5)y-1= 5[x-1/2]Mark this and returnSave and ExitNext​

Accepted Solution

Answer:Point-slope equation of this line:[tex]\displaystyle y - 1 = \frac{1}{2}(x-5)[/tex].Step-by-step explanation:The equation for a line in a cartesian plane can take multiple forms. This question gives a point on the line, andthe slope of the line.The point-slope form will the most appropriate.What is the point-slope form equation of a line [tex]l[/tex]?In general,[tex]l:\; y - y_0 = m (x - x_0)[/tex],where[tex]x_0[/tex] is the x-coordinate of the given point on the line, [tex]y_0[/tex] is the y-coordinate of the given point on the line, and[tex]m[/tex] is the slope or gradient of the line.In other words, [tex](x_0,\; y_0)[/tex]the point on the line.For this line,The point is [tex](5,\;1)[/tex], where [tex]x_0 = 5[/tex] and [tex]y_0 = 1[/tex].Gradient of the line [tex]\displaystyle m = \frac{1}{2}[/tex].Thus the equation for this line:[tex]\displaystyle y - 1 = \frac{1}{2} (x - 5)[/tex].