Answer :
Answer:
[tex]y = -\frac{2}{3}x - 7[/tex]
Step-by-step explanation:
Given
[tex]Point = (6,-11)[/tex]
[tex]Equation: y = -\frac{2}{3}x + 12[/tex]
Required
Determine the equation of the point
First, we need to determine the slope of the point.
Since the point is parallel to the given equation, then they have the same slope (m).
The general form of an equation is:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m = -\frac{2}{3}[/tex]
The equation of the point in slope intercept point is:
[tex]y -y_1 = m(x-x_1)[/tex]
Where
[tex]m = -\frac{2}{3}[/tex]
[tex](x_1,y_1) = (6,-11)[/tex]
Substitute these values in the equation:
[tex]y - (-11) = -\frac{2}{3}(x - 6)[/tex]
[tex]y +11 = -\frac{2}{3}(x - 6)[/tex]
[tex]y +11 = -\frac{2}{3}x + \frac{2}{3}*6[/tex]
[tex]y +11 = -\frac{2}{3}x + 4[/tex]
Subtract 11 from both sides
[tex]y = -\frac{2}{3}x + 4-11[/tex]
[tex]y = -\frac{2}{3}x - 7[/tex]