write an equation of the line containing the given point and parallel to the given line (-2,3)2x=7y+9
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Given point is P: (x1,y1)=(-2,3)
Given line is L: Ax=By+C (2x=7y+9)
A line passing through P and parallel to L is given by:
A(x-x1)=B(y-y1)
rearrange to the form
y=mx+B if possible.
To write the equation of a line parallel to another line, we need to determine the slope of the given line.
First, let's put the given equation in slope-intercept form, which is in the form y = mx + b, where "m" represents the slope.
Start by isolating "y" in the given equation:
2x = 7y + 9
Subtract 9 from both sides:
2x - 9 = 7y
Divide both sides by 7 to isolate "y":
(2x - 9) / 7 = y
Now we have the equation in slope-intercept form: y = (2/7)x - 9/7. We can see that the slope of the given line is 2/7.
Since we want to find the equation of a line parallel to this one, it will also have a slope of 2/7.
Next, we can use the point-slope form of the equation of a line, which is represented as y - y₁ = m(x - x₁), where "m" is the slope and (x₁, y₁) is a point on the line. In this case, the point is (-2, 3).
Substituting the values into the equation, we have:
y - 3 = (2/7)(x - (-2))
Simplifying further:
y - 3 = (2/7)(x + 2)
To get rid of the fraction, we can multiply every term by 7:
7y - 21 = 2(x + 2)
Distributing 2 to both terms inside the parentheses:
7y - 21 = 2x + 4
Now we can rearrange the equation to make it have the standard form, Ax + By = C:
2x - 7y = -25
Therefore, the equation of the line parallel to the given line (-2, 3)2x = 7y + 9 is 2x - 7y = -25.