1. Match the line with the equation it models by choosing one of the following
equations: y= -x , y=x, y=2x , y =0 , x = 0, , y=0.5x , y =x+2
The equation of The parent function line is:
The equation of The y-axis is:
The equation of The x-axis is:
The equation of The reflection of the parent function with respect to y-axis is
The equation of The translation of the parent function line by 2 upwards is
The equation of The rotation of the parent function line around the origin and
the new line is steeper is
The equation of The rotation of the parent function line around the origin and
the new line is less steeper is
2.
Graph each inequality: use https://virtual-graph-paper.com/
a. 2𝑥 + 5𝑦 < 5 𝑎𝑛𝑑 𝑦 > 2
b. 3x +2y > 2 and y < x+1
c. 4𝑦 − 5𝑥 + 6 ≤ 0 𝑎𝑛𝑑 2𝑥 < 𝑦
3. Solve the system of equations to find the point of intersection.
a. y=2/5 x + 7/5 and x =5/2y -7/2
b. -2x+7y-1=0 and y=2/7x +1/7
c. 3x-4y +5 =0 and y =3/4 x + 2
4. Write the equation of the line if the slope is -2 and the x-intercept is 3
5. the coordinates (𝑥1, 𝑦1) of a point on a certain line change if the line is
translated by a vector (3,-5).
a. Describe how
b. If (𝑥1, 𝑦1) = ( 2, 5) , what are the coordinates of the new point
6. Three hours after beginning her long distance bicycle trip, Cathay was 98 Km
from her home. After seven hours after beginning her long distance bicycle trip,
she was 182Km from her home. Assuming she maintained the same speed
throughout the trip, how fast was she cycling?
7. Amin and Ali are both electricians. Amin charges a flat fee of $60 plus $40/hour.
Ali does not charge a flat fee. He just charges $18 per every 20mn of work.
a. Write the equation that models cost with respect to time for each
electrician.
b. Plot the lines on the same grid. What does the point of intersection mean?
c. If you needed an electrician to fix something in your house, who would
you call to do the job?
8. The line y=x with is going through certain transformation
a. It is reflected with respect to the y-axis. rewrite the equation of the new
line and plot both on the same grid.
b.
The line in part a. Is rotated to make it half as steep, write the equation
of the new line
c.
The line in part b. Is translated by 5 upwards. write the equation of the
new line
9. The line y=x is transformed to y= -2 x + 7 using 3 transformations.
Explain all the transformation the line went trough
10. When would you use a dashed line while graphing an inequality? Graph each
inequality:
a. 𝑦 ≥ 5
b. 𝑦 + 2𝑥 ≤ 4
c. 𝑦 ≺ 2 𝑎𝑛𝑑 𝑦 ≺ − 𝑥
11. A graphic designer base charge is $60 and her hourly rate is $40.
a. Write the equation of the relationship and graph it.
b. She wants to change her base rate to $70 and her hourly rate to $45, de
c. scribe how these changes will transform the graph.