# Find the value of t so that the slope of the line passing through the points (2,t) and (6,10)...

## Question:

Find the value of t so that the slope of the line passing through the points (2,t) and (6,10) will be {eq}\frac{1}{2}. {/eq}

## Slope of a Line:

The slope of a line is by how much the line is rising according to the run. The slope of a line that passes through the points {eq}(x_1, y_1) {/eq} and {eq}(x_2, y_2) {/eq} is given by:

$$m= \dfrac{y_2-y_1}{x_2-x_1} $$

## Answer and Explanation:

The given points are:

$$(x_1, y_1) = (2,t) \\ (x_2, y_2)= (6, 10) $$

The slope of the line through these points is given to be: {eq}m= \dfrac{1}{2} {/eq}.

The slope of the line through 2 points is calculated using:

$$m= \dfrac{y_2-y_1}{x_2-x_1} $$

Substituting all the known values in this equation:

$$\dfrac{1}{2}= \dfrac{10-t}{6-2} \\ \dfrac{1}{2} = \dfrac{10-t}{4} \\ \text{Cross multiplying, we get} : \\ 4(1)= 2(10-t) \\ 4= 20-2t \\ \text{Subtracting 20 from both sides},\\ -16=-2t \\ \text{Dividing both sides by -2}, \\ \boxed{\mathbf{t=8}} $$

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