In a line with slope of 3/2 that passes through the point (4,3), what is the y-intercept?
a (-3,0)
b (0,-3)
c (0,0)
d (0,3)
e (3,0)
y=3/2x+b
3=3/2(4)+b
3=6+b
b=-3
y=3/2 x - 3 so when x is zero, y is ...
x = 0
y = -3
Answer : b
Write the equation of the line with a slope of -5 and a y-intercept of (0,3).
To find the y-intercept of a line, we need to determine the value of y when x is equal to 0.
Given that the slope of the line is 3/2 and it passes through the point (4,3), we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope of the line.
Plugging in the values, we have:
y - 3 = (3/2)(x - 4)
Next, we simplify the equation:
y - 3 = (3/2)x - 6
Adding 3 to both sides:
y = (3/2)x - 6 + 3
y = (3/2)x - 3
Now we can easily find the y-intercept by substituting x with 0:
y = (3/2)(0) - 3
y = -3
So the line intersects the y-axis at the point (0, -3).
Therefore, the correct answer is b) (0,-3).