A line L with a slope of 1/4 passes through the points (0,1/2) and (4,y). What is the value of y? This is an SAT prep question, and the answer is supposed to be 3/2 (1.5), but there's no explanation as to how the problem was solved.
slope means for 4 x units, one y advance. You have 4 xunits (4-0), so y goes up 1 to 1.5.
To find the value of y, we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1),
where m is the slope and (x1, y1) are the coordinates of a point on the line.
Given that the slope of line L is 1/4, and it passes through the points (0, 1/2) and (4, y), we can use the point-slope form:
y - 1/2 = (1/4)(x - 0).
Simplifying this equation gives us:
y - 1/2 = (1/4)x.
Now, we can substitute the x-coordinate of the second point, which is 4, and solve for y:
y - 1/2 = (1/4)(4).
y - 1/2 = 1.
Adding 1/2 to both sides of the equation:
y = 1 + 1/2.
y = 3/2.
Therefore, the value of y is 3/2 or 1.5.