Linear Relationships ( hints & questions)

Linear Relationships

SATashkent

​Hints & Questions

• № 1. Start line party at the y-intercept — where x hits zero and y says hello.

  1. What’s the y-intercept in y = 7x - 10?

  2. A gym charges a $15 sign-up fee plus $20 per month. What’s the y-intercept in the cost equation?

  3. If a line hits the y-axis at (0, -3), write its equation assuming slope is 2.

• № 2. Slope is how much y changes when x goes up by 1.

  1. Find the rate of change in y = -4x + 9.

  2. If a plant grows 3 cm every day starting at 5 cm, what’s the slope?

  3. The temperature drops 2 degrees per hour starting at 30°C. Write the equation.

• № 3.Point and slope are like peanut butter and jelly — a classic combo to build your line.

  1. A line passes through the point (1, 4) and has a slope of 3. What is its equation in slope-intercept form?

  2. Write the equation of the line with a slope of –1 that goes through the point (2, –5).

  3. A car is at mile 50 and travels at a constant speed of 60 miles per hour. Let d be the distance and t the time in hours. What is the linear equation relating d and t?

• № 4.Intercepts = graph GPS: y-intercept = cross y-axis, x-intercept = cross x-axis.

  1. Find x-intercept for 4x + 2y = 8.

  2. What’s the y-intercept of y = 6x + 1?

  3. A line crosses x-axis at (3, 0) and y-axis at (0, -2). Write its equation.

• № 5.Zero in on zeros: Find intercepts by plugging in zeros for variables.

  1. Find y-intercept by setting x=0 in y = 2x + 5.

  2. Find x-intercept by setting y=0 in 3x - y = 6.

  3. Line crosses y-axis at 7 and x-axis at -2. Find slope.

• № 6.Rise over run = slope, but don’t forget the ‘sign’ — positive climb, negative slide.

  1. Calculate slope between (2, 10) and (5, 4).

  2. Find slope from (−3, −2) to (1, 6).

  3. What’s slope between (4, 5) and (4, 10)?

• № 7. Write it your way — slope-intercept form: y = mx + b, where m = slope,

  b = y-intercept.

  1. Write line with slope 4, y-intercept -3.

  2. What’s the y-intercept in y = -0.5x + 6?

  3. A line crosses y-axis at 0 and rises 2 for every run of 3. Write the equation.

• № 8. Word problems love fixed fees + per unit charges — build equations like a boss.

  1. A taxi charges $3 base + $2 per mile. Write cost for x miles.

  2. Juice stand sells drinks for $4 each plus $5 stand fee. Write total cost.

  3. Painter charges $100 fixed + $25 per hour. Write the cost after h hours.

• № 9. Tables tell a story — consistent ‘y’ change over ‘x’ means linearity.

  1. Given points (1, 3), (3, 7), (5, 11), find slope.

  2. Does points (2, 4), (4, 8), (6, 10) form a line? Explain.

  3. Create equation from (0, 1), (2, 5), (4, 9).

• № 10. Every point counts! Use any two points to find your line’s slope and then build its equation.

  1. Find slope from (1, 2) and (3, 6) and write the equation.

  2. If a line goes through (−2, 8) and (2, 0), find its equation.

  3. Find the equation passing through (5, −3) with slope −4.

​№1.

1. –10

2. 15

3. y = 2x – 3

№2.

1. –4

2. 3

3. y = –2x + 30

№3.

1. y = 3x + 1

2. y = –x – 3

3. d = 60t + 50

№4.

1. 2

2. 1

3. y = (2/3)x – 2

№5.

1. 5

2. 2

3. 7/2

​№6.

1. –2

2. 2

3. undefined

№7.

1. y = 4x – 3

2. 6

3. y = (2/3)x

№8.

1. C = 3 + 2x

2. C = 5 + 4x

3. C = 100 + 25h

№9.

1. 2

2. No, because the last slope is 1, not 2

3. y = 2x + 1

№10.

1. y = 2x

2. y = –2x + 4

3. y = –4x + 17