y-4 = 2(x-1)
The question asks us to find the point-slope form of a line with the points (1, 4) and (2, 6).
The point-slope equation of a line is one of many equations relating variables x and y to create a particular line when graphed.
We need two components to use the point-slope equation: a point on the line and the line's slope.
We already have a point on the line (the question tells us to use the first one in our equation). Now, we need to find the slope.
The equation to find the slope of the line when given two points, commonly referred to as rise over run, is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The points given in the question will be [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
We can plug the x and y values of the points into the slope equation and solve for [tex]m[/tex]:
[tex]m=\dfrac{6-4}{2-1}=\dfrac{2}{1}=\boxed{2}[/tex]
Now that we have the components needed for the point-slope form, we can plug them into the point-slope equation:
[tex]y-y_1=m(x-x_1)\\\boxed{y-4=2(x-1)}[/tex]
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