Mathematics: Slope-intercept form of the equation for the line?

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Slope-intercept form of the equation for the line?

hadwell34

09.03.2022

$\large\boxed{y=-\dfrac{3}{10}x+\dfrac{1}{2}}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept

The formula of a slope:

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

We have the points from the graph (-5, 2) and (5, -1).

Substitute:

$m=\dfrac{-1-2}{5-(-5)}=\dfrac{-3}{10}=-\dfrac{3}{10}$

We have the equation in form:

$y=-\dfrac{3}{10}x+b$

Put the coordinates of the point (5, -1) to the equation:

$-1=-\dfrac{3}{10}(5)+b$

$-1=-\dfrac{3}{2}+b$

$-\dfrac{2}{2}=-\dfrac{3}{2}+b$ add 3/2 to both sides

$\dfrac{1}{2}=b\to b=\dfrac{1}{2}$

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