Write the slope-intercept form equation of a line parallel to y - 1 = -3/5(x - 5) and passes through the point (-5, -1)
To find the slope-intercept form equation of a line parallel to a given line, we need to determine the slope and the y-intercept of the new line.
Given that the line we want to find is parallel to the line y - 1 = -3/5(x - 5), we know that its slope will be the same as the given line's slope, which is -3/5.
Next, we need to find the y-intercept of the new line. We can do this by substituting the coordinates of the given point (-5, -1) into the equation and solving for the y-intercept.
Using the given point (-5, -1) in the slope-intercept equation y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope, we have:
y - (-1) = -3/5(x - (-5))
y + 1 = -3/5(x + 5)
To convert this equation into the slope-intercept form of y = mx + b, we can simplify it further:
y + 1 = -3/5x - 3
y = -3/5x - 3 - 1
y = -3/5x - 4
Therefore, the slope-intercept form equation of the line parallel to y - 1 = -3/5(x - 5) and passing through the point (-5, -1) is y = -3/5x - 4.
To find the slope-intercept form equation of a line parallel to a given line and passing through a given point, we need to use two pieces of information: the slope of the given line and the coordinates of the given point.
The given line is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. By comparing the given equation, y - 1 = -3/5(x - 5), to the slope-intercept form, we can see that the slope of the given line is -3/5.
Since the line we're looking for is parallel to the given line, it will have the same slope. Therefore, the slope of the line we're looking for is also -3/5.
Now, let's use the coordinates of the given point (-5, -1) to find the y-intercept (b) of the line we're looking for. We can substitute the coordinates into the slope-intercept form (y = mx + b) and solve for b.
Using the coordinates, we have -1 = (-3/5)(-5) + b.
Simplifying this, we get -1 = 3 + b.
To isolate b, let's subtract 3 from both sides: -1 - 3 = b.
This becomes -4 = b.
Now we have both the slope (-3/5) and the y-intercept (b = -4) of the line we're looking for. We can plug these values into the slope-intercept form to obtain the equation.
Therefore, the slope-intercept form equation of the line parallel to y - 1 = -3/5(x - 5) and passing through the point (-5, -1) is y = (-3/5)x - 4.