Find the equation of line $b$ described below, in slope-intercept form.
Line $a$ is parallel to line $b$.
Line a passes through the points $(1,3)$ and $(2,-7)$.
Line b passes through the point $(5,12)$.
The equation of line $b$ is $y=$
(Simplify your answer. Type an expression using $x$ as the variable. Use integers or fractions for any numbers in the expression.)
Answer
\(\boxed{y = -10x + 62}\)
Step 1 ：First, find the slope of line a using the formula: \(slope = \frac{y2 - y1}{x2 - x1}\)
Step 2 ：\(slope_a = \frac{-7 - 3}{2 - 1} = -10\)
Step 3 ：Since line a is parallel to line b, the slope of line b is also -10.
Step 4 ：Next, find the y-intercept of line b using the point-slope form of a linear equation: \(y - y1 = m(x - x1)\), where m is the slope and (x1, y1) is the point (5, 12) that line b passes through.
Step 5 ：\(y - 12 = -10(x - 5)\)
Step 6 ：\(y - 12 = -10x + 50\)
Step 7 ：\(y = -10x + 62\)
Step 8 ：\(\boxed{y = -10x + 62}\)
