Calculus- Early Transcendentals, 2021a

30 Review
To determine a, we substitute one of the points into the equation and solve. Let us substitute the point
(x,y)=(−4,24) into the equation:
Therefore, the equation of the parabola is:
24 − (−1)=a(−4 − 1) 2 → 25 = 25a → a = 1.
y + 1 =(x − 1) 2 .
Note that if we substituted (7,35) into the equation instead, we would also get a = 1.
♣
Exercises for 1.2
Exercise 1.2.1 Find the equation of the line in the form y = mx + b:
(a) through (1,1) and (−5,−3).
(b) through (−1,2) with slope −2.
(c) through (−1,1) and (5,−3).
(d) through (2,5) and parallel to the line 3x + 9y + 6 = 0.
(e) with x-intercept 5 and perpendicular to the line y = 2x + 4.
Exercise 1.2.2 Change the following equations to the form y = mx + b, graph the line, and find the y-
intercept and x-intercept.
(a) y − 2x = 2
(b) x + y = 6
(c) x = 2y − 1
(d) 3 = 2y
(e) 2x + 3y + 6 = 0
Exercise 1.2.3 Determine whether the lines 3x + 6y = 7 and 2x + 4y = 5 are parallel.
Exercise 1.2.4 Suppose a triangle in the xy-plane has vertices (−1,0), (1,0) and (0,2). Find the equations
of the three lines that lie along the sides of the triangle in y = mx + bform.
Exercise 1.2.5 Let x stand for temperature in degrees Celsius (centigrade), and let y stand for temperature
in degrees Fahrenheit. A temperature of 0 ◦ C corresponds to 32 ◦ F, and a temperature of 100 ◦ C corresponds
to 212 ◦ F. Find the equation of the line that relates temperature Fahrenheit y to temperature Celsius x in