write an equation of the line containing the given point and parallel to the given line (7,9);x+7y=4
To find an equation of a line parallel to the given line, we need to determine the slope of the given line. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope.
To find the slope of the given line x + 7y = 4, we need to rewrite it in slope-intercept form.
Start by isolating y by subtracting x from both sides of the equation:
7y = -x + 4
Next, divide both sides of the equation by 7 to solve for y:
y = (-1/7)x + 4/7
The slope, m, of this line is -1/7.
Since the parallel line has the same slope, we can use the point-slope form of an equation, y - y1 = m(x - x1), to write the equation. The given point (7,9) will be used as (x1,y1) in the equation.
Substituting the values, we get:
y - 9 = (-1/7)(x - 7)
Now, we can simplify the equation further:
y - 9 = (-1/7)x + 1
Finally, we can rearrange the equation in slope-intercept form:
y = (-1/7)x + 10
Therefore, the equation of the line containing the point (7,9) and parallel to the line x + 7y = 4 is y = (-1/7)x + 10.