Write the equation of a line in slope-intercept form that is parallel to the line y = 3x +2 and passes through the point (5, 2).
To find the equation of a line that is parallel to y = 3x + 2, we know that the slope of the new line will also be 3.
Using the point-slope form of a linear equation, we can write the equation as:
y - y1 = m(x - x1)
where (x1, y1) represents the given point (5, 2) and m is the slope.
Plugging in the values we have, the equation becomes:
y - 2 = 3(x - 5)
Expanding the equation, we get:
y - 2 = 3x - 15
or
y = 3x - 13
So, the equation of the line parallel to y = 3x + 2 and passing through the point (5, 2) is y = 3x - 13.
To find the equation of a line that is parallel to y = 3x + 2 and passes through the point (5, 2), we can use the fact that parallel lines have the same slope.
The given line y = 3x + 2 is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the given line has a slope of 3. Therefore, the parallel line we are looking for will also have a slope of 3.
Now that we know the slope for the parallel line, we can use the point-slope form of a linear equation to find the equation of this line. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (5, 2), we can substitute the values into the equation:
y - 2 = 3(x - 5)
Now, we can simplify and rearrange the equation to find it in slope-intercept form:
y - 2 = 3x - 15
Adding 2 to both sides:
y = 3x - 13
Therefore, the equation of the line that is parallel to y = 3x + 2 and passes through the point (5, 2) is y = 3x - 13.
y = mx + b
2 = 3*5 + b
b = -13
y = 3x - 13