write y = - 3x - 6; ( -1, 5) in an equation of a line parallel to the given line but passing through the given point
y-5 = -3(x+1)
To find the equation of a line parallel to the given line and passing through the given point, we can follow these steps:
Step 1: Understand the problem
The given line is y = -3x - 6, and the given point is (-1, 5). We need to find an equation for a line that has the same slope as the given line (since parallel lines have the same slope) and passes through the point (-1, 5).
Step 2: Find the slope of the given line
The equation of the given line is in slope-intercept form (y = mx + b), where m represents the slope of the line. Comparing the equation y = -3x - 6 to y = mx + b, we can see that the slope of the given line is -3.
Step 3: Use the slope-intercept form of a line
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Since we already know the slope of the line (-3), we need to find the y-intercept (b) to get the equation of the line.
Step 4: Substitute the point into the equation
Since the line passes through the point (-1, 5), we can substitute these values into the equation y = -3x + b and solve for b.
5 = (-3)(-1) + b
5 = 3 + b
b = 5 - 3
b = 2
Step 5: Write the equation
Now that we have the values for both the slope (m = -3) and the y-intercept (b = 2), we can write the equation of the line parallel to the given line that passes through the point (-1, 5).
Therefore, the equation of the line parallel to y = -3x - 6 and passing through the point (-1, 5) is:
y = -3x + 2.