The pair of points (7,4) and (3,y) lie on the line with a slope of 1/4. What is the value of y.
A.20
B.-12
C.-3
D.3
(y - 4) / (3 - 7) = 1 / 4
solve for y
Joe
To find the value of y, we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Given that the slope is 1/4 and one point is (7,4), we can substitute the values into the formula:
1/4 = (y - 4) / (3 - 7)
Simplifying the equation further:
1/4 = (y - 4) / -4
Cross-multiplying:
-4 = y - 4
Adding 4 to both sides:
0 = y
Therefore, the value of y is 0.
None of the options provided in the question match this result, so none of the given options is correct.
To find the value of y, we need to use the slope-intercept form of a linear equation, which is y = mx + b.
Given that the slope of the line is 1/4, we can substitute m = 1/4 into the equation:
y = (1/4)x + b.
Next, we can substitute the coordinates of one of the given points (7,4) into the equation, where x = 7 and y = 4:
4 = (1/4)(7) + b.
To find the value of b, we can solve this equation for b:
4 = 7/4 + b.
Multiply both sides of the equation by 4 to eliminate the fraction:
16 = 7 + 4b.
Subtract 7 from both sides of the equation:
16 - 7 = 4b.
9 = 4b.
Divide both sides of the equation by 4 to solve for b:
b = 9/4.
Now that we have the value of b, we can substitute it back into the equation of the line:
y = (1/4)x + 9/4.
To find the value of y when x = 3, substitute x = 3 into the equation:
y = (1/4)(3) + 9/4.
Simplify the expression to find the value of y:
y = 3/4 + 9/4.
y = (3 + 9)/4.
y = 12/4.
y = 3.
Therefore, the value of y is 3.
The answer is D. 3.