Answer:
[tex]\displaystyle y = -\frac{2}{3}\, x - 3[/tex].
Step-by-step explanation:
The given line [tex]y = (-2/3)\, x + 6[/tex] is in the slope-intercept form: [tex]y = m\, x + b[/tex], where [tex]m[/tex] denotes the slope of the line and [tex]b[/tex] denotes the [tex]y[/tex]-intercept.
For [tex]y = (-2/3)\, x + 6[/tex], the slope would be [tex]m = (-2/3)[/tex].
Two lines in a cartesian plane are parallel if and only if their slopes are the same. Thus, if the line in question is parallel to [tex]y = (-2/3)\, x + 6[/tex], the other line should also have a slope of [tex](-2/3)[/tex].
If a line in a cartesian plane has slope [tex]m[/tex] and goes through the point [tex](x_{0},\, y_{0})[/tex], the equation of that line in point-slope form would be:
[tex]y - y_{0} = m\, (x - x_{0})[/tex].
Since the line in question has slope [tex]m = (-2/3)[/tex] and goes through the point [tex](6,\, -7)[/tex] (for which [tex]x_{0} = 6[/tex] and [tex]y_{0} = -7[/tex],) the equation of that line in point-slope form would be:
[tex]\displaystyle y - (-7) = \left(-\frac{2}{3}\right)\, (x - 6)[/tex].
Rearrange to obtain the equation of the same line in slope-intercept form:
[tex]\displaystyle y = -\frac{2}{3}\, x - 3[/tex].
Alternative solution to a similar question: https://brainly.com/question/26833404.
Answer:
[tex]\displaystyle 2x + 3y = -9\:or\: y = -\frac{2}{3}x - 3[/tex]
Step-by-step explanation:
Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so –⅔ remains as is as you move forward plugging the information into the Slope-Intercept formula:
[tex]\displaystyle -7 = -\frac{2}{3}[6] + n \hookrightarrow -7 = -4 + b; -3 = b \\ \\ \boxed{y = -\frac{2}{3}x - 3}[/tex]
Suppose you need to write this equation in standard form. Do the following:
y = –⅔x - 3
+ ⅔x + ⅔x
___________
⅔x + y = –3 [We CANNOT leave the equation like this, so multiply by 3 to eradicate the fraction.]
3[⅔x + y = –3]
[tex]\displaystyle 2x + 3y = -9[/tex]
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