SAT Mathematics Practice Test 7

Since the line passes through the point (2, 0), its equation is of the form y = m(x − 2). The coordinates of thepoint (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 $\frac{4-0}{1-2}=-4$. 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.