write an equation for the line parallel to the given line that contains C.
C(-3,7); y=8/9x +7
To find an equation for a line parallel to the given line that contains point C(-3,7), we need to consider that parallel lines have the same slope.
First, let's find the slope of the given line. The given line has the equation y = (8/9)x + 7, which is in slope-intercept form (y = mx + b), where m is the slope. By comparing the equation to the standard slope-intercept form, we can determine that the slope of the given line is 8/9.
Since the parallel line has the same slope, the equation of the line passing through point C(-3,7) can be written as y = (8/9)x + b, where b is the y-intercept that we need to find.
To find b, substitute the coordinates of point C(-3,7) into the equation:
7 = (8/9)(-3) + b
Simplifying the expression:
7 = -8/3 + b
To isolate b, multiply both sides of the equation by 9 (the common denominator of 9 and 3):
7 * 9 = -8/3 * 9 + 9b
63 = -24 + 9b
Next, add 24 to both sides of the equation:
63 + 24 = 9b
87 = 9b
Finally, divide both sides of the equation by 9 to solve for b:
87/9 = b
9.67 ≈ b
Therefore, the equation of the line parallel to the given line that contains point C(-3,7) is y = (8/9)x + 9.67.
To find an equation for a line parallel to the given line, we need to use the fact that parallel lines have the same slope.
The given line has a slope of 8/9, so the parallel line will also have a slope of 8/9.
Using the point-slope form of a linear equation, we can write the equation for the parallel line:
y - y₁ = m(x - x₁)
where (x₁, y₁) are the coordinates of point C, and m is the slope.
Substituting the values into the equation, we have:
y - 7 = 8/9(x - (-3))
Simplifying:
y - 7 = 8/9(x + 3)
Now, we can multiply through by 9 to eliminate the fraction:
9y - 63 = 8(x + 3)
Expanding the equation:
9y - 63 = 8x + 24
To get the equation into the standard slope-intercept form (y = mx + b), we need to isolate y:
9y = 8x + 24 + 63
9y = 8x + 87
Dividing both sides by 9:
y = (8/9)x + 87/9
Simplifying the equation gives the final answer:
y = (8/9)x + 9.67
y = 8/9x + c
7 = 8/9(-3) + c
7 = -24/9 + c
29/3 = c
y = 8/9x + 29/3