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The graph of a line in the xy-plane passes through the point (1, 4) and crosses the x-axis at the point (2, 0). The line crosses the y-axis at the point (0, b).
What is the value of b ?
What is the value of b ?
Correct answer is '8'. Can you explain this answer?
Most Upvoted Answer
The graph of a line in the xy-plane passes through the point (1, 4) an...
The correct answer is 8. Since the line passes through the point (2, 0), its equation is of the form y = m(x − 2). The coordinates of the point (1, 4) must also satisfy this equation. So 4 = m(1 − 2), or m = −4. Substituting −4 for m in the equation of the line gives y = −4(x – 2), or equivalently y = −4x + 8. Therefore, b = 8.
Alternate approach: Given the coordinates of two points through which the line passes, the slope of the line is
= −4. So, the equation of the line is of the form y = −4x + b. Since (2, 0) satisfies this equation, 0 = −4(2) + b must be true. Solving this equation for b gives b = 8.
Alternate approach: Given the coordinates of two points through which the line passes, the slope of the line is
= −4. So, the equation of the line is of the form y = −4x + b. Since (2, 0) satisfies this equation, 0 = −4(2) + b must be true. Solving this equation for b gives b = 8.Free Test
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Community Answer
The graph of a line in the xy-plane passes through the point (1, 4) an...
Given:
- The line passes through the point (1, 4).
- The line crosses the x-axis at the point (2, 0).
- The line crosses the y-axis at the point (0, b).
To find:
The value of b.
Approach:
We can find the equation of the line using the given information and then determine the value of b.
Step 1: Finding the slope of the line
The line passes through the points (1, 4) and (2, 0). We can use the slope formula to find the slope of the line.
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (1, 4) and (2, 0):
m = (0 - 4) / (2 - 1)
m = -4 / 1
m = -4
Step 2: Finding the equation of the line
We can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
Using the point (1, 4) and the slope -4:
y - 4 = -4(x - 1)
y - 4 = -4x + 4
y = -4x + 8
So, the equation of the line is y = -4x + 8.
Step 3: Finding the value of b
To find the value of b, we need to determine the y-coordinate when x = 0 (since the line crosses the y-axis at the point (0, b)).
Substituting x = 0 in the equation of the line:
y = -4(0) + 8
y = 8
Therefore, the value of b is 8.
Final Answer:
The value of b is 8.
- The line passes through the point (1, 4).
- The line crosses the x-axis at the point (2, 0).
- The line crosses the y-axis at the point (0, b).
To find:
The value of b.
Approach:
We can find the equation of the line using the given information and then determine the value of b.
Step 1: Finding the slope of the line
The line passes through the points (1, 4) and (2, 0). We can use the slope formula to find the slope of the line.
The slope formula is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (1, 4) and (2, 0):
m = (0 - 4) / (2 - 1)
m = -4 / 1
m = -4
Step 2: Finding the equation of the line
We can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
Using the point (1, 4) and the slope -4:
y - 4 = -4(x - 1)
y - 4 = -4x + 4
y = -4x + 8
So, the equation of the line is y = -4x + 8.
Step 3: Finding the value of b
To find the value of b, we need to determine the y-coordinate when x = 0 (since the line crosses the y-axis at the point (0, b)).
Substituting x = 0 in the equation of the line:
y = -4(0) + 8
y = 8
Therefore, the value of b is 8.
Final Answer:
The value of b is 8.
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The graph of a line in the xy-plane passes through the point (1, 4) and crosses the x-axis at the point (2, 0). The line crosses the y-axis at the point (0, b).What is the value of b ?Correct answer is '8'. Can you explain this answer?
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