Given an equation of a line, find equations for lines parallel or perpendicular to it going through specified points. Find the appropriate equations and points from the table below. Simplify your equations into slope-intercept form.
The equation is y=3x+3 (-1,_-1)
Slope intercept form: y=mx+b. Having the equation y=3x+3 its already in slope intercept form.
for the parallel line, you have a slope and a point, so use the point-slope form to get
y+1 = 3(x+1)
The perp. line has slope -1/3, so it is
y+1 = -1/3 (x+1)
Now massage those into slope-intercept form.
what is the equation of the through (-6, -5) and (-4, -4) in slope inercept form
To find equations for lines parallel or perpendicular to the given line y = 3x + 3, we need to determine the slope of the given line, as well as the desired points that the new lines should pass through.
The given line equation is already in slope-intercept form (y = mx + b), where m is the slope of the line. So we can easily determine the slope of the given line as 3.
1. To find the equation for a line parallel to the given line, with a known point (-1, -1), we can use the point-slope form of a line: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point.
Let's substitute the values into the equation:
y - (-1) = 3(x - (-1))
y + 1 = 3(x + 1)
y + 1 = 3x + 3
y = 3x + 2
Therefore, the equation for the line parallel to y = 3x + 3 and passing through (-1, -1) is y = 3x + 2.
2. To find the equation for a line perpendicular to the given line, with a known point (-1, -1), we can first determine the negative reciprocal of the slope of the given line, which will be the slope of the perpendicular line.
The negative reciprocal of 3 is -1/3.
Using the point-slope form again, we get:
y - (-1) = (-1/3)(x - (-1))
y + 1 = (-1/3)(x + 1)
To simplify this equation, we can multiply both sides by 3 to eliminate the fraction:
3(y + 1) = -1(x + 1)
3y + 3 = -x - 1
3y = -x - 4
y = (-1/3)x - (4/3)
Therefore, the equation for the line perpendicular to y = 3x + 3 and passing through (-1, -1) is y = (-1/3)x - (4/3).
In summary:
The equation for the line parallel to y = 3x + 3 and passing through (-1, -1) is y = 3x + 2.
The equation for the line perpendicular to y = 3x + 3 and passing through (-1, -1) is y = (-1/3)x - (4/3).