Answer:
[tex]\boxed {\boxed {\sf E. \ y=x-3}}[/tex]
Step-by-step explanation:
To find the equation of the line, we must first find the slope, then use the point-slope formula.
1. Find the Slope
The slope formula is the change in y over the change in x, or:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where (x₁, y₁) and (x₂, y₂) are the points the line passes through.
The points given in the problem are (6,3) and (4,1). Therefore:
[tex]x_1=6 \\y_1=3 \\x_2=4 \\y_2=1[/tex]
Substitute the values into the formula.
[tex]m=\frac{1-3}{4-6}[/tex]
Solve the numerator.
[tex]m=\frac{-2}{4-6}[/tex]
Solve the denominator.
[tex]m=\frac{-2}{-2}[/tex]
Divide.
[tex]m=1[/tex]
2. Find the Equation of the Line
We have the slope and a point, so we can use the point-slope formula.
[tex]y-y_1=m(x-x_1)[/tex]
We know the slope is 1 and we can pick either point to use for (x₁, y₁). Let's use (4,1).
[tex]y-1=1(x-4)[/tex]
Distribute the 1.
[tex]y-1=(1*x)+(1*-4)\\y-1=x-4[/tex]
We want to find the equation in y=mx+b, so we must isolate the variable on one side of the equation.
1 is being subtracted from y and the inverse of subtraction is addition. Add 1 to both sides of the equation.
[tex]y-1+1=x-4+1\\y=x-4+1\\y=x-3[/tex]
In slope-intercept form, the equation of the line is y=x-3
