Hello!
To find the line parallel to the line y = -2/3x + 1 and passing through the point (-6, -1), we will need to know that if two lines are parallel, then their slopes are equivalent to each other.
Since we are given the slope, we need to find the y-intercept of the line. We can find the y-intercept by substituting the point (-6, -1) into a new equation with the slope of m = -2/3. Remember that slope-intercept form is y = mx + b.
y = -2/3x + b (substitute the ordered pair)
-1 = -2/3(-6) + b
-1 = 4 + b (subtract 4 from both sides)
-5 = b
Therefore, the equation of the line passing through the point (-6, -1) and parallel to y = -2/3x + 1 is y = -2/3x - 5.
Linear equation with the given information is
[tex]y=-\frac{2}{3}x-5\\[/tex]
Given :
The line Passing through (-6,-1) and parallel to [tex]y=- \frac{2}{3} x +1[/tex]
Equation of a line in the form y=mx+b
where m is the slope
From the given equation [tex]y=- \frac{2}{3} x +1[/tex]
Slope is [tex]-\frac{2}{3}[/tex]
Slope of parallel lines are same. Slope of parallel line is [tex]-\frac{2}{3}[/tex]
Now we find out y intercept b using equation y=mx+b
use the given point (-6,-1) that is our x and y
[tex]y=-\frac{2}{3}x+b\\-1=-\frac{2}{3}(-6)+b\\\\-1=4+b\\-1-4=b\\b=-5[/tex]
Linear equation with the given information is
[tex]y=-\frac{2}{3}x-5\\[/tex]
Learn more : brainly.com/question/18518952
