Ch3L5 Linear Equation-Point-Slope Form

Question 1

Point-Slope form: given a point P1(x1,y1) and slope=m, what is the equation for this linear equation?

Answer 1

y-y1 = m(x-x1)

Question 2

Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of days that have passed.

Question 3

Julio plans a diet to gain 0.2 kg a day. After 14 days he weighs 40 kg. The number days he diets and his weight are related.

Question 4

when a pair of the value of (x,y) and constant m/slope are given, how to figure out the equation?

Question 5

If a line pass through point (8,1) and point (-2,9). Write an equation in Point-slope form.

Question 6

The cost of assistant dog training will change according to the number of sessions for this training. If the dog is trained 5 sessions, then it will cost you $165. And if the session is 10, then it will cost you $290. Write an equation in the Point-slope form for this.

Question 7

Jack is planning a party. The cost for 20 people is $290 and cost for 45 people is $590. Write an equation in Point-Slope form for this situation.

Question 8

After 2 seconds on a penalty kick in soccer game, the ball travels 160 feet. After 2.75 seconds on the same kick, the ball travels 220 feet. Write an equation in Point-Slope form for this situation.

Question 9

The equation of line is y = 2x+6. Write it in Point-Slope form

Question 10

After 4 hours of driving, Jan is 248 miles away from home. After 6 hours of driving, she is 372 miles away from home. Write an equation in Point-Slope form to show the distance to her home and time she drives.

Question 11

Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86. The cost of the call and the length of the call are related.

Question 12

Biologists have found that the number of chirps some crickets make per minute is related to temperature. The relationship if very close to being linear. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit.

Question 13

when a pair of the value of P1(x1,y1) and constant b(y-intercept) are given, how to figure out the equation?

Answer 13

First, from y-intercept to get intersect point between this line and y-Axis: P0(0,y-intercept)

Then, using P1 and P0 to calculate slope

slope = rise/run

=(y1-y-intercept)/(x1-0)

So, the Slope-Intercept form of eqation is:

y=slope*x+y-intercept

Question 14

given P1(1,1) and y-intercept is 2. write down the slope-intercept form of the equation;

Answer 14

First, use y-intercept value to find intersect of the line and y-Axis: P0(0,2)

Then, use P0 and P1 to get slope;

slope = (1-2)/(1-0) = -1

So, the slope-intercept form of equation is:

y = -x+ 2

or y = 2 - x