Respuesta :
Given the following coordinates of the two points that pass through the line.
Point 1 : 0, - 2
Point 2 : 2, 1
Let's determine the equation of the line:
Step 1: Let's determine the slope (m).
[tex]\text{ Slope = m = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{1\text{ - (-2)}}{2\text{ - 0}}[/tex][tex]\text{ m = }\frac{1\text{ + 2}}{2}\text{ = }\frac{3}{2}[/tex]Step 2: Let's determine the y - intercept (b). Using the slope-intercept form: y = mx + b, plug in m = 3/2 and x,y = 0, -2.
[tex]\text{ y = mx + b}[/tex][tex]\text{ -2 = (}\frac{3}{2})(0)\text{ + b}[/tex][tex]\text{ b = -2}[/tex]Step 3: Let's complete the equation. Plug in m = 3/2 and b = -2 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (}\frac{3}{2})x\text{ + (-2)}[/tex][tex]\text{ y = }\frac{3}{2}x\text{ - 2}[/tex]Therefore, the equation of the line is:
[tex]\text{ y = }\frac{3}{2}x\text{ - 2}[/tex]