How do you calculate the slope of (0,0) and (2,6)?

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Answer 1 · 2015-08-21T11:40:45

$m = 3$ $m = 3$

For two points written in the general form

$(x_{1}, y_{1})$ $color(blue)((x_1"," y_1))" "$ and $(x_{2}, y_{2})$ $" "color(blue)((x_2"," y_2))$

the slope of the line that passes through both of these points is defined as

$slope = m = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})}$ $color(blue)("slope" = m = ((y_2 - y_1))/((x_2 - x_1)))$

In your case, you have

${(x_1 = 0), (y_1 = 0) :}" "$ and $" "{(x_2 = 2), (y_2 = 6) :}$ .

This means that the slope will be equal to

$m = (6 - 0)/(2 - 0) = 6/2 = color(green)(3)$

To plot the line, use the formula

$color(blue)(y - y_i = m * (x- x_i))$

Plug in the coordinates of one of the two points to get

$y - y_1 = m * (x-x_1)$

$y - 0 = 3 * (x - 0)$

$y = 3x$

graph{3x [-10, 10, -5, 5]}