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a line has a slope of -2/3 and passes through the point -3,8 how do I get the equation ?

Sagot :

Answer:

The equation of the line in slope-intercept form is;

[tex]y=-\frac{2}{3}x+6[/tex]

Explanation:

We want to find the equation of the line with the slope and a point given.

[tex]\begin{gathered} \text{slope m=}\frac{-2}{3} \\ \text{ point (-3,8)} \end{gathered}[/tex]

Recall that the point-slope equation of a straight line is of the form;

[tex]y-y_1=m(x-x_1)[/tex]

substituting the given slope and point into the equation and simplifying;

[tex]\begin{gathered} y-8=-\frac{2}{3}(x-(-3)) \\ y-8=-\frac{2}{3}(x+3) \\ y=-\frac{2}{3}x-\frac{2}{3}(3)+8 \\ y=-\frac{2}{3}x-2+8 \\ y=-\frac{2}{3}x+6 \end{gathered}[/tex]

Therefore, the equation of the line in slope-intercept form is;

[tex]y=-\frac{2}{3}x+6[/tex]