Answer :
To be able to find the y-intercept and the equation of the line of JM, let's identify at least two points that the pass-through line JM and use it in getting the slope, y-intercept, and equation in Slope-Intercept Form: y = mx + b.
Let's use Point J and Point L.
Point J = x1,y1 = (0,6)
Point L = x2,y2 = (6,2)
Step 1: Let's determine the slope of the line (m).
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1_{}}[/tex][tex]m\text{ = }\frac{2\text{ - 6}}{6\text{ - 0}}\text{ = }\frac{-4}{6}\text{ = -}\frac{\frac{4}{2}}{\frac{6}{2}}[/tex][tex]m\text{ = -}\frac{2}{3}[/tex]Step 2: Let's determine the y-intercept (b). Substitute m = -2/3 and x,y = 0,6 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 6 = (-}\frac{2}{3})(0)\text{ + b}[/tex][tex]\text{ 6 = 0 + b}[/tex][tex]\text{ b = 6}[/tex]Step 3: Let's complete the equation. Substitute m = -2/3 and b = 6 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (-}\frac{2}{3})x\text{ + (6)}[/tex][tex]\text{ y = -}\frac{2}{3}x\text{ + 6}[/tex]Therefore, the y-intercept of the line containing M is 6 and the equation of the line is y = -2x/3 + 6.