Find the equation of the line parallel to 3x-y=7 that passes through the point (9,2)
a.y=3x-25
b.y=3x+25
c.y=-1/3x+5
d.y=-1/3x+25
slope = 3
so,
y-2 = 3(x-9)
To find the equation of a line parallel to a given line, we need to find the slope of the given line first.
The equation of the given line is 3x - y = 7. We need to rewrite this equation in the form of y = mx + b (slope-intercept form), where m represents the slope and b represents the y-intercept.
To do that, let's rearrange the equation:
-y = -3x + 7
y = 3x - 7
From this equation, we can see that the slope of the given line is 3.
Now, we can use the point-slope form to find the equation of the parallel line that passes through the point (9,2).
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 have:
y - 2 = 3(x - 9)
Expanding and rearranging this equation, we get:
y - 2 = 3x - 27
y = 3x - 25
Therefore, the equation of the line parallel to 3x - y = 7 that passes through the point (9,2) is:
a. y = 3x - 25
To find the equation of a line parallel to the given line, we need to know that parallel lines have the same slope. In this case, the given line has a slope of 3.
The equation of a line can be written in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the line parallel to 3x - y = 7, we first need to rearrange the given equation to get it in slope-intercept form.
3x - y = 7
=> y = 3x - 7
Now we know that the slope of the line we're looking for is 3. We also have a point that this line passes through, which is (9,2).
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values into the equation to find the equation of the line.
y - 2 = 3(x -9)
Next, we can simplify and solve for y:
y - 2 = 3x - 27
Adding 2 to both sides:
y = 3x - 25
Therefore, the equation of the line parallel to 3x - y = 7 that passes through the point (9, 2) is y = 3x - 25, option a.