Given the following points that pass through a line:
Let,
Point A : (-3, 3)
Point B : (1, 5)
Let's determine the equation of the line in Slope-Intercept Form: y = mx + b
Step 1: Let's determine the slope of the line (m).
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\text{ }\frac{5\text{ - 3}}{1\text{ - (-3)}}\text{ = }\frac{5\text{ - 3}}{1\text{ + 3}}[/tex][tex]m\text{ = }\frac{2}{4}\text{ = }\frac{1}{2}[/tex]Step 2: Let's determine the y-intercept (b). Substitute m = 1/2 and x,y = 1,5 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 5 = (}\frac{1}{2})(1)\text{ + b}[/tex][tex]5\text{ - }\frac{1}{2}\text{ = b}[/tex][tex]\frac{10}{2}\text{ -}\frac{1}{2\text{ }}\text{ = b}[/tex][tex]\text{ }\frac{9}{2}\text{ = b}[/tex]Step 3: Let's complete the equation. Substitute m = 1/2 and b = 9/2 in y = mx + b.
[tex]\text{ y = (}\frac{1}{2})x\text{ + (}\frac{9}{2})[/tex][tex]\text{ y = }\frac{1}{2}x\text{ + }\frac{9}{2}[/tex]Therefore, the equation of the line is y = 1/2x + 9/2.
