Writing Equations in Slope-Intercept Form (y=mx + b)
A line has a slope of ½ and a y-intercept of -3. What is the equation of the line in y = mx + b form?
Y = 1/2x – 3
Write an equation in point-slope form of the line that passes through (2,7) and has the slope of -4.
y -7 = -4(x - 2)
Classify the pair of equations. Explain (Parallel, Perpendicular, Neither)
y = ⅓ x - 3
y = -3x - 12
Perpendicular
⅓ is the reciprocal of -3
The number of fish in a pond 3 months after being stocked was 1,200. 8 months after being stocked, the number of fish had decreased to 700. Write an equation that relates the number of fish, y, that are in the pond “x” months after being stocked.
y = -100x + 1,500
A line has a slope of 4 and passes through the point (0, 3). What is the equation of the line in y = mx + b form?
y = 4x + 3
Write an equation in point-slope form of the line that passes through (7, -6) and has the slope of ½.
y + 6 = ½ (x - 7)
Classify the pair of equations. Explain. (Parallel, Perpendicular, Neither)
y = ⅕ x + 3
y = ⅕ - 6
Parallel
The slope is the same.
A candle’s height after 2 hours of burning is 18 inches and 6 inches after 8 hours of burning. Write an equation that relates the height of the candle, H(t) after “t” hours.
H(t) = -2t + 22
A line has a slope of 5 and passes through the point (1, 3). What is the equation of the line in slope-intercept form? (HINT: you must solve for the y-intercept)
y = 5x – 2
Graph the equation y + 4 = -3(x + 2)
Show graph
Classify the pair of equations. Explain. (Parallel, Perpendicular, Neither)
-x + y = -2
y -11 = (x -2)
Parallel = same slope
-x + y = -2 y -11 = (x -2)
+x +x +11 +11
y = x -2 y = x + 9
A students starts with $20 in a savings account and saves money at a constant rate. After 4 weeks, the account balance is $36. After 10 weeks, the balance is $60.
Write an equation that represents the amount of money in the account, S(t), after t weeks.
How much money is in the account account after 7 weeks?
1. S(t) = 4t +20
2. S(7) = 48
A line passes through the points (4, 2) and (6, 8). Write an equation for the line in slope-intercept form.
(HINT: start by finding the slope of the line).
y = 3x - 10
Write an equation in the point -slope form of the line graphed below.
y- 3 = -¼ (x - 4)
Classify the pair of equations. Explain. (Parallel, Perpendicular, Neither)
-x + y = 6
y - 6 = - (x - 4)
Perpendicular = slopes are opposite reciprocals
-x + y = 6 y - 6 = - (x + 4)
+x +x +6 +6
y= x - 6 y = -x + 10
After 4 games, a basketball player scored 28 points. He continued to score the same amount for the next couple games. After 10 games, the player scored 58 point.
Write an equation that represents the total number of points scored, P(g), after g games.
How many total points will the player have after 15 games?
1. P(g) = 5(g) + 8
2. P(g) = 83
A line passes through points (4, 7), (6, 10) and (8, 13). Find an equation for the line in slope-intercept form.
(HINT: Pick 2 of the points and calculate the slope.
y = 3/2x + 1
Write an equation in point-slope form of the line that passes (4,7) and (5, 1). Use the first point to write the equation.
y – 7 = -6(x – 4)
Write the slope-intercept form of the equation of the line.
through: (2,-4 ), parallel to y= 3x + 2
y = 3x - 10
FInd the equation of a line in slope- intercept form that is parallel to the graph of y = 2x + 4 and passes through (8,-4).
y = 2x - 20