Question
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
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
Answers
Answer
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?
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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.
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.
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