How do you determine the the missing coordinate of A(_, 0), B(5, 10) if the slope is 2?

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Answer 1 · 2015-06-13T21:15:36

$x_{1} = 0$ $x_1=0$

Consider that the slope $m$ $m$ is:
$m=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)$
In your case:
$m=2=(10-0)/(5-x_1)$
so that rearranging:
$x_1=0$

Answer 2 · 2015-06-13T21:20:37

Let $(x_1, y_1) = A = (x_1, 0)$ and $(x_2, y_2) = B = (5, 10)$

Then slope $2 = m = (Delta y)/(Delta x) = (y_2 - y_1) / (x_2 - x_1) = (10-0)/(5-x_1) = 10/(5-x_1)$

Hence $x_1 = 0$

Slope $m$ is given by the formula:

$m = (Delta y)/(Delta x) = (y_2 - y_1)/(x_2 - x_1)$

where the line passes through points $(x_1, y_1)$ and $(x_2, y_2)$

In our example, we are given $m$ , $y_1$ , $x_2$ and $y_2$ and we are trying to find the value of $x_1$ .

Putting our known values into the equation for slope, we get:

$2 = (10-0)/(5-x_1) = 10/(5-x_1)$

Multiply both ends by $(5-x_1)$ to get:

$10 = 2(5 - x_1) = 10 - 2x_1$

Subtract $10$ from both sides to get:

$-2x_1 = 0$

Divide both sides by $-2$ to get:

$x_1 = 0$