Write an equation of the line passing through point P(4,0) that is parallel to the line -x +2y = 12
the given line has slope 1/2
So, now you have a point and a slope, so the equation is
y = 1/2 (x-4)
Write an equation of the line passing through the point \left(-10,\ 3\right) that is parallel to the line 5x+2y=12.
Why did the line go to the therapist? Because it was feeling parallelly depressed! Anyway, let's find the equation you're looking for.
The given equation, -x + 2y = 12, can be rewritten as 2y = x + 12, or y = (1/2)x + 6. Since we want a line parallel to this, the slope must be the same, which is 1/2.
Using the slope-intercept form (y = mx + b) and substituting the coordinates of point P(4,0), we have y = (1/2)x + b. Plugging in x = 4 and y = 0, we get 0 = (1/2)(4) + b.
Solving for b, we have 0 = 2 + b, so b = -2.
Therefore, the equation of the parallel line passing through point P(4,0) is y = (1/2)x - 2.
To find the equation of a line parallel to the given line, we need to determine the slope of the given line. The equation is already in the form Ax + By = C, where A = -1, B = 2, and C = 12. The slope of a line can be found by rearranging the equation to solve for y:
-x + 2y = 12
2y = x + 12
y = (1/2)x + 6
So, the slope of the given line is 1/2.
Since the line we want to find is parallel to the given line, it will have the same slope. Now, we can use the point-slope form of the equation of a line to find the equation.
The equation of a line in point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents a point on the line, and m represents the slope.
Plugging in the values, we have:
y - 0 = (1/2)(x - 4)
Simplifying further, we get:
y = (1/2)x - 2
Therefore, the equation of the line passing through point P(4, 0) that is parallel to the line -x + 2y = 12 is y = (1/2)x - 2.