Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y = mx + b.
(2,3); x + 6y = 7
The equation of the line is y =________
To find the equation of a line parallel to the given line, we need to determine the slope of the given line first. The given line is x + 6y = 7.
To convert the equation into slope-intercept form (y = mx + b), we can isolate y by subtracting x from both sides and then dividing by 6:
6y = -x + 7
y = (-1/6)x + 7/6
Now, we can see that the slope of the given line is -1/6.
Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope of the line we want to find is also -1/6.
Next, we can use the point-slope form of a linear equation to find the equation of the line passing through the given point (2,3) with a slope of -1/6:
y - y1 = m(x - x1)
Substituting the values of the point (2,3) and the slope -1/6:
y - 3 = (-1/6)(x - 2)
Expanding the equation:
y - 3 = (-1/6)x + 1/3
To express the equation in the required form (y = mx + b), we can add 3 to both sides:
y = (-1/6)x + 1/3 + 3
Simplifying further:
y = (-1/6)x + 1/3 + 9/3
Combining the fractions:
y = (-1/6)x + 10/3
Therefore, the equation of the line parallel to x + 6y = 7 and passing through the point (2,3) is y = (-1/6)x + 10/3.
Find the slope:
6y=-x+7
y=-1/6 x + 7
so m=-1/6
Next, put the point in y=mx + b, and solve for b.