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Sagot :
From the given, it shows two points that pass through the given graph. These points are:
Point A : x1, y1 = 4, 1
Point B : x2, y2 = 5, 2
We will be using these points in generating the equation of the line.
Step 1: Let's determine the slope m of the line.
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{\text{ 2 - 1}}{\text{ 5 - 4}}\text{ = }\frac{1}{1}\text{ = 1}[/tex]Step 2: Let's determine the y-intercept b. Substitute x,y = 4, 1 and m = 1 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 1 = (1)(4) + b}[/tex][tex]\text{ 1 = 4 + b}[/tex][tex]\text{ 1 - 4 = b}[/tex][tex]\text{ -3 = b}[/tex]Step 3: Let's complete the equation. Substitute m = 1 and b = -3 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (1)x + (-3)}[/tex][tex]\text{ y = x - 3}[/tex]Therefore, the equation of the line is y = x - 3.
The answer is letter B.
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