9What are the x- and y-intercepts for a line with one point at (2,1) and another at (6,3)?[graph with two points
AThe x-intercept is (2,1) and the y-intercept is (5,3)
BThe x-intercept is (0,1) and the y-intercept is (3,0)
CThe x-intercept is (0,2) and the y-intercept is (4,0)
DBoth the x and y intercepts are (0,0)
The x-intercept is the point where the line crosses the x-axis, which means the y-coordinate is 0. The y-intercept is the point where the line crosses the y-axis, which means the x-coordinate is 0.
To find the x-intercept, we set y = 0 and solve for x. Plugging in the coordinates (2,1) and (6,3), we get:
0 = m(2) + b
0 = m(6) + b
This gives us a system of equations. Solving for m and b, we find:
m = (3 - 1) / (6 - 2) = 2/4 = 1/2
b = 0 - (1/2)(2) = -1
So the equation of the line is y = (1/2)x - 1.
To find the x-intercept:
0 = (1/2)x - 1
1 = (1/2)x
x = 2
Therefore, the x-intercept is (2, 0). This eliminates options A, B, and C.
To find the y-intercept:
Set x = 0 in the equation y = (1/2)x - 1:
y = (1/2)(0) - 1
y = -1
Therefore, the y-intercept is (0, -1). So, the answer is not D.
The correct answer is option B: The x-intercept is (0,1) and the y-intercept is (3,0).