What is the equation in slope-intercept form of the line that passes through the point (5,0) and is parallel to the line represented by y=12/5x+18/5?
What is the equation in slope-intercept form of the line that passes through the point (5,0) and is parallel to the line represented by y=12/5x+18/5?
y=12/5x-12
y=12/5x+5
y=-12/5x+5
y=-12/5x+12
To find the equation of the line that is parallel to y = (12/5)x + (18/5) and passes through (5,0), we need to use the fact that parallel lines have the same slope.
The given equation is in slope-intercept form, y = mx + b, where m represents the slope.
In the given equation, y = (12/5)x + (18/5), the slope is 12/5.
Therefore, for the parallel line, the slope will also be 12/5.
The equation of the line through (5,0) with a slope of 12/5 is:
y = (12/5)x + b
To find the value of b, substitute the x and y coordinates of the point (5,0) into the equation:
0 = (12/5)(5) + b
0 = 12 + b
b = -12
The equation of the line passing through (5,0) and parallel to y = (12/5)x + (18/5) is:
y = (12/5)x - 12
Therefore, the correct answer is: y = (12/5)x - 12.
To find the equation in slope-intercept form of the line that is parallel to the given line and passes through the point (5,0), we need to use the fact that parallel lines have the same slope.
First, let's find the slope of the given line. The given line is represented by the equation y = (12/5)x + 18/5. Since this equation is already in slope-intercept form (y = mx + b), we can see that the slope of the line is 12/5.
Since we want to find a parallel line, which has the same slope, the slope of our desired line is also 12/5.
Now, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plug in the values:
y - 0 = (12/5)(x - 5)
Simplify:
y = (12/5)(x - 5)
Distribute 12/5:
y = (12/5)x - (12/5)(5)
Simplify:
y = (12/5)x - 12
Therefore, the equation in slope-intercept form of the line that passes through the point (5,0) and is parallel to the given line is y = (12/5)x - 12.
To find the equation of a line that is parallel to another line, we need to use the same slope.
The given line has the equation y = (12/5)x + 18/5. The slope of this line is 12/5.
Using the point-slope form of a line, 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 of the point (5,0) and the slope 12/5.
Therefore, the equation of the line passing through (5,0) and parallel to the given line is:
y - 0 = (12/5)(x - 5)
Simplifying:
y = (12/5)(x - 5)
y = (12/5)x - (12/5)(5)
y = (12/5)x - 12
So, the equation in slope-intercept form of the line that passes through the point (5,0) and is parallel to the line represented by y = (12/5)x + 18/5 is y = (12/5)x - 12.
What is the equation in slope-intercept form of the line that passes through the point (1,5) and is parallel to the line represented by 3x-y=4?
To find the equation of a line that is parallel to the given line, we need to determine the slope of the given line first. The given equation is in standard form, 3x - y = 4.
To rewrite the equation in slope-intercept form (y = mx + b), we need to isolate y:
3x - y = 4
-y = -3x + 4
y = 3x - 4
So, the slope of the given line is 3.
Since the desired line is parallel to the given line, it will also have a slope of 3.
Now, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values (1,5) for (x1, y1) and 3 for m:
y - 5 = 3(x - 1)
Simplify:
y - 5 = 3x - 3
Add 5 to both sides:
y = 3x + 2
Therefore, the equation in slope-intercept form of the line that passes through the point (1,5) and is parallel to the given line is y = 3x + 2.