Write the equation of the line that passes through the given point and is parallel to the given line. Your answer should be written in slope-intercept form.
P(−9, 3), y + 6x = −20
To find the equation of a line parallel to another line, we need to determine the slope of the given line and then use the point-slope form to write the equation in slope-intercept form.
The given line is y + 6x = -20. Let's rearrange this equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
To do that, subtract 6x from both sides of the equation:
y = -6x - 20.
Since the new line is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also -6.
Now, we can use the point-slope form, y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Plugging in the values into the point-slope form, we have:
y - 3 = -6(x - (-9)).
Simplifying the equation further:
y - 3 = -6(x + 9).
Expanding the brackets:
y - 3 = -6x - 54.
Finally, rearrange the equation in slope-intercept form:
y = -6x - 51.
Therefore, the equation of the line passing through point P(-9, 3) and parallel to the given line y + 6x = -20 is y = -6x - 51.
To find the equation of a line parallel to a given line, we need to determine the slope of the given line first.
The given line equation is y + 6x = −20. To get the equation in slope-intercept form, we need to isolate y.
y + 6x = −20
y = -6x - 20
Now, we can see that the slope of the given line is -6, which means any line parallel to the given line will also have a slope of -6.
Now that we have the slope (-6) and a point that the line passes through (P(-9, 3)), we can use the point-slope form of a line to find the equation.
The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line.
Plugging in the values, we have:
y - 3 = -6(x - (-9))
Simplifying further, we get:
y - 3 = -6(x + 9)
Expanding the brackets:
y - 3 = -6x - 54
Now, let's rearrange the equation to get the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Adding 6x to both sides of the equation:
6x + y - 3 = -54
Rearranging the terms:
y = -6x - 51
So, the equation of the line that passes through the point P(-9, 3) and is parallel to the line y + 6x = −20 is y = -6x - 51.
again, start with the point-slope form, since they gave you a point and a slope.
y-3 = -6(x+9)
y = -6x-51