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 ?

Explanation

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 `(4-0)/(1-2)=-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.