slope
what is the slope of a horizontal line?
0
what is the y-intercept of the line that passes through the points (-3,5) and (2,-1)
7
how do you graph a linear equation using its slope and y-intercept
y=MX+B
what do all the variables mean in MX+B
M= slope of the line
B= y-int.
suppose you want to buy some apples and bananas. Apples cost $0.50 each, and bananas cost $0.25 each. You have $5 to spend, and you want to buy at least 10 pieces of fruit. How many apples and bananas can you buy?
A= APPLES
B= BANANAS
A+B>=10
0.5A+0.25B<=5(can't spend more than 5)
SOLVE USING substitution for A
A>=10-B
0.5(10-5)+0.25B<=5
SECOND EQUATION
0.5(10-B)+0.25B<=5
5-0.5B+0.25B<=5
0.25B<=0
B<=0
CANT BUY ANY BANANAS
A>=10-B
A>=10-0
A>=10
BUY AT LEAST 10 APPLES CANT BUY ANY BANANAS
what is the slope of a Vertical line?
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what is the y-intercept of a line with an equation of y= 2x-4
-4
how do you find the slope of a line given two points on the line? GIVE THE FORMULA
M=(Y2-Y1)/(X2-X1)
how do you find the intersection point of two lines given their equations?
1. write the two equations in slope-intercept form
2. set the two equal and solve for X
3. Substitute the value of X into one of the original equations to find the value of y
4. check your answer by plugging both values into both equations
Suppose you work at a coffee shop that sells two sizes of coffee: small and large. A small coffee costs $2.50 and a large coffee costs $3.75. One day, you sell 100 coffees for a total of $300. How many small and large coffees did you sell?
S+L=100
2.5s+3.75L =300
ELIMINATION
-2.5S-2.5L=-250
-2.5S-2.5L + 2.5+ 3.75L =-250 +300
1.25L=50
L=40
40 LARGE COFFEES
S+L=100S+40=100
S=60
60 small coffees60 small coffees and 40 large coffees
what is the slope of a line that passes through the points of (2,3) and (4,5)?
1
what is the y-intercept of the line that passes through the points (0,3) and (4,1)
3
how do you determine if two lines are parallel or perpendicular given their equations?
look at the slopes of the lines, if slopes are equal then the lines are parallel. If the slopes are negative reciprocals of each other then the lines are perpendicular
what is the difference between a consistent and an inconsistent system of linear equations?
Consistent- has at least one solution, number of solutions can be one or infinitely many
Inconsistent- has no solution
suppose you want to mix two types of nuts to make a trail mix. type A nuts cost &4.50 per pound, and type B nuts cost $6.25 per pound. You want to make 20 pounds of trail mix that costs $5.75 per pound. How many pounds of each type of nut should you use?
A=TYPE A
B+TYPE B
A+B=20
4.5A+6.25B=5.75*20
A=20-B
4.5(20-B)+6.25B=5.75 *20
90-4.5B+6.25B=115
1.75B=25
B=14.29
about 14.29 pounds of type B
TYPE A
A+B=20
A+14.29=20
A=5.71
5.71 pounds of Type A nuts
Type A- 5.71 pounds
Type B- 14.29
what is the slope of a line that passes through the points of (-5,-2) and (1,4)?
1.5
what is the y-intercept of the line with an equation of y=-0.5x+6
6
what is the standard form of a linear equation?
Ax+By=C
what are the steps to solve a system of linear equations using substitution?
1. write the equations in standard form
2. choose one variable to eliminate by adding or subtracting the equation. Multiply one or both of the equations by a constant
3. add or subtract the equations to eliminate the chosen variable
4. solve for the remaining variable
5. Substitute the value of the variable into one of the original equations to find the value of the eliminated variable
6. check you answer by plugging both values into both equations
Suppose you are trying to save money to buy a new car. You are currently have $10,000 in savings, and you want to save a total of $25,000. You plan to save a fixed amount of money each month, and you expect to earn 2% interest on your saving each year. How much should you save each month to reach your goal in 3 years?
total amount= $10,000+36(x+0.02/12*$10,000)=25,000
x=(25,000-10,000)/36 - 0.02/12*10,000
x=$416.67
you should save about $416.67 each month to reach your goal of $25,00 in 3 years
what is the slope of a line that is perpendicular to a line with a slope of 2?
-0.5
if a line has a y-intercept of 7 and a slope of -3, what is the equation of the line?
y=-3x+7
what is the point-slope form of a linear equation?
y-y1=m(x-x1)
what are the steps to solve a linear equation using substitution?
1. solve one of the equations for one of the variables in terms of the other variable
2. Substitute the expression you found for the variable into the other equation, replacing that variable with the expression
3. simplify the resulting equation by distributing any constants or coefficients, and combining like terms
4. solve the resulting equations for the remaining variable
5. Substitute the value you found for the second variable back into either of the original equations, and solve for the other variable
6. check your answer by substituting both values into both original equations
Suppose you are planning to buy a new smartphone that costs $800, and you want to pay for it in installments over 2 years. The store offers a payment plan with no interest, where you pay a fixed amount each month for 24 months. How much should you pay off the phone in 2 years?
Total cost= $800
x*24=$800
x=$800/24
x=$33.33
you should pay about $33.33 each month