How do you find the slope of the line that passes through (2.5,3), (1,-9)?

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Answer 1 · 2018-03-21T14:18:33

Slope (m): $= 8$ $color(blue)(=8$

Equation of the line passing through the points $(2.5, 3), (1, - 9)$ $color(red)((2.5, 3),(1,-9)$ is given by

$y = 8 x - 17$ $color(blue)(y=8x-17)$

Given:

We are given the two points $(2.5, 3), (1, - 9)$ $color(red)((2.5, 3),(1,-9)$

These points are $(x_{a}, y_{1}), (x_{2}, y_{2})$ $color(blue)((x_a,y_1), (x_2,y_2)$

Slope-Intercept form of the equation of the line is

$y = m x + b$ $color(green)(y = mx+b$ , $m$ $color(red)(m$ being the Slope.

We must find the values of $a and b$ $color(brown)(a and b)$ to write the equation of the line.

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

$m = \frac{- 9 - 3}{1 - 2.5} = 8$ $m=(-9-3)/(1-2.5)=8$

Substitute this value of $m = 8$ $color(red)(m=8$ in $y = m x + b$ $color(blue)(y = mx+b$ , using the point $(1, - 9) .$ $color(green)((1,-9).$

We get,

$- 9 = 8 \cdot 1 + b$ $-9=8*1+b$

$- 9 = 8 + b$ $-9=8+b$

Add $(- 8)$ $color(red)((-8)$ to both sides of the equation.

$- 9 + (- 8) = 8 + b + - 8$ $-9+color(red)((-8))=8+b+color(red)(-8$

$-9+color(red)((-8))=cancel(8)+b+color(red)(-cancel(8)$

$-17=b$

Hence,

$b=-17$ . Observe that this is the y-intercept of the line.

Use the value of the slope $(m) = 8$ and $b=-17$ to obtain the equation of the line passing through the two points, in $y = mx+b$

We get,

$color(blue)(y = 8x-17$

Hence,

Equation of the line passing through the points $color(red)((2.5, 3),(1,-9)$ is given by

$color(blue)(y=8x-17)$

Hope it helps.