Question

5-91. use the given information to write the equation of each line.
a. has a slope of 2 and passing through (10,17).
b. passing through (1,−4) and (−2,5).

Explanation:

Step1: Use point-slope form (part a)

Point-slope formula: $y - y_1 = m(x - x_1)$, where $m=2$, $(x_1,y_1)=(10,17)$
$y - 17 = 2(x - 10)$

Step2: Simplify to slope-intercept (part a)

Expand and isolate $y$:
$y - 17 = 2x - 20$
$y = 2x - 20 + 17$
$y = 2x - 3$

Step3: Calculate slope (part b)

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)=(1,-4)$, $(x_2,y_2)=(-2,5)$
$m = \frac{5 - (-4)}{-2 - 1} = \frac{9}{-3} = -3$

Step4: Use point-slope form (part b)

Substitute $m=-3$, $(x_1,y_1)=(1,-4)$:
$y - (-4) = -3(x - 1)$

Step5: Simplify to slope-intercept (part b)

Expand and isolate $y$:
$y + 4 = -3x + 3$
$y = -3x + 3 - 4$
$y = -3x - 1$

Answer:

a. $y = 2x - 3$
b. $y = -3x - 1$