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10 ptsWrite an equation in slope - intercept form for the line that passes through the given paint andis parallel to the given equation.5.(-2, 3), y =-3/4x+4

Sagot :

Two lines are parallel if:

[tex]m1=m2[/tex]

For the line:

[tex]\begin{gathered} y=-\frac{3}{4}x+4 \\ \text{Its slope is:} \\ m1=-\frac{3}{4} \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} m2=m1 \\ m2=-\frac{3}{4} \end{gathered}[/tex]

Let:

(x1,y1)=(-2,3)

Using the point slope equation:

[tex]\begin{gathered} y-y1=m(x-x1) \\ y-3=-\frac{3}{4}(x+2) \\ y-3=-\frac{3}{4}x-\frac{3}{2} \\ y=-\frac{3}{4}x-\frac{3}{2}+3 \\ y=-\frac{3}{4}x+\frac{3}{2} \end{gathered}[/tex]

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