What is -2/5 as y=mx=b form or into slope intercept form

1 answer:

5 0

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~{{ -5}} &,&{{ -1}}~) 
% (c,d)
&&(~{{ 5}} &,&{{ -5}}~)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}\implies 
\cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{-5-(-1)}{5-(-5)}\implies \cfrac{-5+1}{5+5}\implies \cfrac{-4}{10}
\\\\\\
 -\cfrac{2}{5}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=-\cfrac{2}{5}[x-(-5)]
\\\\\\
y+1=-\cfrac{2}{5}(x+5)\implies y+1=-\cfrac{2}{5}x-\cfrac{2}{\underline{5}}\cdot \underline{5}\implies y+1=-\cfrac{2}{5}x-2
\\\\\\
y+1-1=-\cfrac{2}{5}x-2-1\implies y=-\cfrac{2}{5}x-3$

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What is the equation of the line that passes through (-3, -1) and has a slope of 2/5 ? Put your answer in slope-intercept form.

Scrat [10]

Answer:

a. y = 2/5x + 1/5

Step-by-step explanation:

In point-slope form, the equation of a line with slope m through point (h, k) can be written

y = m(x -h) +k

Then a line with slope 2/5 through the point (-3, -1) will have point-slope equation ...

y = (2/5)(x +3) -1

This can be simplified to the desired form:

y = 2/5x +6/5 -1 . . . . . . eliminate parentheses; next, collect terms