Answer :
Given the following points that pass through a graph.
Point 1: (6, 2)
Point 2: (8, 8)
Let's determine the equation of the line.
Step 1: Determine the slope.
[tex]\text{ Slope = m = }\frac{y_2\text{ - y}_1}{x_2\text{ - x}_1}[/tex][tex]\text{ = }\frac{8\text{ - 2}}{8\text{ - 6}}\text{ = }\frac{6}{2}[/tex][tex]\text{ Slope = m = 3}[/tex]Step 2: Let's determine the y-intercept (b). Plugin m = 3 and x,y = 6, 2 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 2 = \lparen3\rparen\lparen6\rparen + b}[/tex][tex]\text{ 2 = 18 + b}[/tex][tex]\text{ b = 2 - 18 = -16}[/tex]Step 3: Let's complete the equation. Plugin m = 3 and b = -16 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = \lparen3\rparen x + \lparen-16\rparen}[/tex][tex]\text{ y = 3x - 16}[/tex]Therefore, the equation of the line is y = 3x - 16
