Write an equation of the line that passes through (-5,-1) and is parallel to the line y=-3x+6
The only thing that will change is the constant, since the slope has to stay at -3
so the new equation is y = -3x + b
plug in your new point (-5,-1)
-1 = -3(-5) + b
-1 = 15 + b
-16 = b
so your new equation is y = -3x - 16
your line has slope of -3
So, now you have a point and a slope, so use the point-slope form of the new line:
y+1 = -3(x+5)
To find the equation of a line that is parallel to the given line, we first need to determine the slope of the given line.
The equation y = -3x + 6 is in slope-intercept form (y = mx + b), where m represents the slope of the line. In this case, the slope of the given line is -3.
Since parallel lines have the same slope, our new line will also have a slope of -3.
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the new line. The point-slope form is given by:
y - y1 = m(x - x1),
where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.
In this case, we are given the point (-5, -1) and the slope -3. Plugging the values into the point-slope form, we get:
y - (-1) = -3(x - (-5)).
Simplifying this equation, we have:
y + 1 = -3(x + 5).
Expanding the right side of the equation, we get:
y + 1 = -3x - 15.
Finally, rearranging the equation into slope-intercept form, we have:
y = -3x - 16.
Therefore, the equation of the line that passes through (-5, -1) and is parallel to the line y = -3x + 6 is y = -3x - 16.