what is an equation of the line that passes through the points (6, 3) and (-6, 1)?
what is an equation of the line that passes through the points (6, 3) and (-6, 1)?
Answer
Explanation:
Step1: Find the slope (m)
The formula for slope ( m ) between two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Substituting ( (x_1, y_1)=(6, 3) ) and ( (x_2, y_2)=(- 6, 1) ), we get: ( m=\frac{1 - 3}{-6 - 6}=\frac{-2}{-12}=\frac{1}{6} )
Step2: Use point - slope form to find the equation
The point - slope form of a line is ( y - y_1=m(x - x_1) ). Let's use the point ( (6, 3) ) (we could also use ( (-6,1) )). Substitute ( m = \frac{1}{6} ), ( x_1 = 6 ) and ( y_1 = 3 ) into the point - slope form: ( y-3=\frac{1}{6}(x - 6) ) Expand the right - hand side: ( y-3=\frac{1}{6}x-1 ) Add 3 to both sides: ( y=\frac{1}{6}x+2 ) We can also write it in standard form ( Ax + By=C ). Multiply through by 6 to get ( x-6y=-12 ) (or keep it in slope - intercept form ( y=\frac{1}{6}x + 2 ))