(-4,8);6x=7y+3 Write the equation of the line containing the given points and parallel to given line express your answer in y=mx+b form
The line has slope 6/7
So, using the point-slope form of a line,
(y-8)/(x+4) = 6/7
y-8 = 6/7 (x+4)
y - 8 = 6/7 x + 24/7
y = 6/7 x + 80/7
or
7y = 6x + 80
To find the equation of a line parallel to the given line that passes through the given points, we need to determine the slope (m) and the y-intercept (b) of the line.
First, let's find the slope of the given line. The equation 6x = 7y + 3 is in the form y = mx + b. To convert it to this form, let's isolate y:
6x = 7y + 3
7y = 6x - 3
y = (6/7)x - 3/7
From the equation, we can see that the slope (m) of the given line is 6/7.
Since the line we are trying to find is parallel to the given line, it will have the same slope, meaning its slope (m) will also be 6/7.
Now, we can use the point-slope form of a line to find the equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Using the point (-4, 8) that is given, we can substitute the values into the point-slope form:
y - 8 = (6/7)(x - (-4))
y - 8 = (6/7)(x + 4)
To express the equation in y = mx + b form, we need to simplify it further:
y - 8 = (6/7)x + 24/7
y = (6/7)x + 24/7 + 8
y = (6/7)x + (24/7 + 56/7)/7
y = (6/7)x + 80/7
Therefore, the equation of the line containing the given points (-4, 8) and parallel to the given line 6x = 7y + 3 is y = (6/7)x + 80/7.