Point Slope Form
Is the following equation an example of line in point slope form?
y = -2x+1
No, this is in slope intercept form.
Is the following equation an example of line in slope-intercept form?
3x-y= 5
No, this equation is in standard form
Is the following equation an example of a line that is standard form?
y-7 = 2(x+4)
No, this line is in point-slope form.
A delivery service charges a base fee of $5 plus $2.50 for each package delivered. If the total cost for delivering a certain number of packages is $25, determine how many packages were delivered.
8 packages were delivered.
We need to use the equation
2.50(p)+5=T(p)
p=\text{package}
T(p)=\text{total cost}
Create the equation of line with slope m=4 and y-intercept=-5.
y=4x-5
Is the following equation in slope intercept form?
y = x^2+5x+1
No, this is not point-slope form.
Bonus: This is not a linear function.
What is the equation for a line in slope intercept form?
y=mx+b
m=slope
b=\text{ y-intercept}
Is the following equation an example of a line in standard form
y= 4x-2
No, the following equation is in slope-intercept form.
A youth club is organizing a camping trip. The initial number of boys signed up is 40, and each week, 2 more boys join the trip. How long will it take to for there to be 100 boys signed up?
30 weeks
Use the equation
2(w)+40 = T(w)
w=\text{weeks}
T(w)=\text{Total number of boys}
Create the equation of line that will pass through the points (3,5) and (-1,2).
y=3/4x+11/4
y-5=3/4(x-3)
Is the following function an example of a function in point-slope form
y-4 = -2(x+3)
Yes, this is point slope form.
Is the following equation an example of line in slope-intercept form?
y= 3x
Yes, this equation in slope intercept form.
slope is 3 and the y-intercept is (0,0)
Is the following equation an example of line in standard form
3x+4/3y=4
No, not all coefficients or constants are not integers.
The sum of Maria's age and twice her sisters' age is 36. Write an linear equation to represent the relationship and determine Maria's age if her sister is 8 years old.
The relationship between the sisters age can be modeled with the equation
m+2s=36
Maria's age is 20 years old
Create the equation of line that will pass through the point (1,-5) and will be parallel to the line
y=-2/3x+7
y+5=-2/3(x-1)
What is the equation for line in point-slope form?
y-y_1=m(x-x_1)
m =slope
(x_1,y_1) \text{ is the point}
IS the following equation an example of slope intercept form
y= e^{2x+2}
No, this equation is not in slope-intercept form.
Bonus: This is not linear, and it an example of a exponential function.
Is the following equation an example of a line that is in standard form
-4x+7y = 2
No, the coefficient of the x-variable is less than zero (negative) it must be positive.
A taxi service charges a fixed fee of $8 plus $1.75 for each mile traveled. If the total cost of a taxi ride is $25, determine the number of miles traveled.
number of miles traveled is approximately 9.71 miles.
use the equation
1.75m+8 = T(m)
m=\text{miles}
T(x) =\text{total cost}
Suppose that we have two numbers where the sum of twice the first number and 4 times the second number is 17. What is an equation that can represent the relationship between these two numbers?
2x+4y=17
Is the point (4,3) on the line
y- 6= -2(x+4)
No, the point (4,3) is not on the line.
Is the point (0,0) on the equation
y=-5x+3
No, the point does not lie on the line
convert the following equation from slope intercept form to standard form
y= 2/3 x+4
2x-3y=-12
Alice has $50 and decides to save $5 each week. Bob has no savings initially bust saves $8 each week. After how many weeks will Alice and bob have the same amount of money saved
At about 17 weeks Alice and Bob will have the same amount of money.
Use the equations
A(t) = 5t+50, t=\text{weeks}
B(t) = 8t, t=\text{weeks}
Convert the following equation into Standard form and slope-intercept form:
y-7=-2/5(x-3)
y=-2/5x+29/5
2x+5y=29