what is the equation of a line that is parallel to the line y=2/3x+5 and passes through (6.3)
To find the equation of a line parallel to the line y = (2/3)x + 5 and passing through the point (6,3), you first need to determine the slope of the parallel line.
The slope of the given line in slope-intercept form (y = mx + b) is 2/3. Since parallel lines have the same slope, the slope of the line parallel to y = (2/3)x + 5 is also 2/3.
Now, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Plugging in the values y1 = 3, x1 = 6, and m = 2/3, we get:
y - 3 = (2/3)(x - 6)
Simplifying further:
y - 3 = (2/3)x - (2/3)(6)
y - 3 = (2/3)x - 4
Finally, adding 3 to both sides of the equation:
y = (2/3)x - 4 + 3
Therefore, the equation of the line parallel to y = (2/3)x + 5 and passing through the point (6,3) is y = (2/3)x - 1.
To find the equation of a line that is parallel to the given line and passes through the point (6,3), we can use the fact that parallel lines have the same slope.
The given line has a slope of 2/3. So the parallel line will also have a slope of 2/3.
Now we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values into the equation, we get:
y - 3 = (2/3)(x - 6)
Now, let's simplify the equation:
y - 3 = (2/3)(x - 6)
y - 3 = (2/3)x - (2/3)(6)
y - 3 = (2/3)x - 4
y = (2/3)x - 1
So, the equation of the line that is parallel to y = (2/3)x + 5 and passes through the point (6,3) is y = (2/3)x - 1.
slope is 2/3, so using the point-slope form,
y-3 = 2/3 (x-6)