3.4 – Slope & Direct Variation
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Transcript of 3.4 – Slope & Direct Variation
3.4 – Slope & Direct Variation
3.4 – Slope & Direct Variation• Direct Variation:
3.4 – Slope & Direct Variation• Direct Variation: y = kx
3.4 – Slope & Direct Variation• Direct Variation: y = kx
(k = constant of variation)
3.4 – Slope & Direct Variation• Direct Variation: y = kx
(k = constant of variation)
Reads:
3.4 – Slope & Direct Variation• Direct Variation: y = kx
(k = constant of variation)
Reads: “y varies directly with x.”
3.4 – Slope & Direct Variation• Direct Variation: y = kx
(k = constant of variation)
Reads: “y varies directly with x.”
– Direct Variation Equations ALWAYS go through the origin!!!
3.4 – Slope & Direct Variation• Direct Variation: y = kx
(k = constant of variation)
Reads: “y varies directly with x.”
– Direct Variation Equations ALWAYS go through the origin!!!
– Constant of Variation = Slope
3.4 – Slope & Direct Variation• Direct Variation: y = kx
(k = constant of variation)
Reads: “y varies directly with x.”
– Direct Variation Equations ALWAYS go through the origin!!!
– Constant of Variation = Slope, so k = m!
Ex. 1 Graph y = 4x
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 =
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 = 4
1
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 = 4
1
2) Graph (0,0)
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 = 4
1
2) Graph (0,0)
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 = 4
1
2) Graph (0,0)
3) Use slope to find next
point.
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 = 4
1
2) Graph (0,0)
3) Use slope to find next
point.
4
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 = 4
1
2) Graph (0,0)
3) Use slope to find next
point.
1
4
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 = 4
1
2) Graph (0,0)
3) Use slope to find next
point.
1
4
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 = 4
1
2) Graph (0,0)
3) Use slope to find next
point.
4) Draw line through points
1
4
Ex. 1 Graph y = 4x1) Write the slope as a ratio.
4 = 4
1
2) Graph (0,0)
3) Use slope to find next
point.
4) Draw line through points
1
4
Ex. 2 Graph y = -½x
Ex. 2 Graph y = -½x1) Write the slope as a ratio.
2) Graph (0,0)
3) Use slope to find next
point.
4) Draw line through points
Ex. 2 Graph y = -½x1) Write the slope as a ratio.
-1
2
2) Graph (0,0)
3) Use slope to find next
point.
4) Draw line through points
-1
2
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.
1) Write equation:
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.
1) Write equation: y = kx
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.
1) Write equation: y = kx
8 = k(4)
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.
1) Write equation: y = kx
8 = k(4)
8 = 4k
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.
1) Write equation: y = kx
8 = k(4)
8 = 4k
k = 2
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.
1) Write equation: y = kx
8 = k(4)
8 = 4k
k = 2, so y = 2x
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.
1) Write equation: y = kx
8 = k(4)
8 = 4k
k = 2, so y = 2x
2) Plug in given value, solve for missing!
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.
1) Write equation: y = kx
8 = k(4)
8 = 4k
k = 2, so y = 2x
2) Plug in given value, solve for missing!
y = 2x
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.1) Write equation: y = kx
8 = k(4) 8 = 4k
k = 2, so y = 2x2) Plug in given value, solve for missing!
y = 2x y = 2(5)
• Write a direct variation equation that relates x and y. Assume that y varies directly with x. Then solve.
Ex.3 If y = 8 when x= 4, find y when x= 5.1) Write equation: y = kx
8 = k(4) 8 = 4k
k = 2, so y = 2x2) Plug in given value, solve for missing!
y = 2x y = 2(5)y = 10
Ex.4 If y = 36 when x = 6, find x when y = 42
Ex.4 If y = 36 when x = 6, find x when y = 42
1) Write equation:
2) Plug in given value, solve for missing!
Ex.4 If y = 36 when x = 6, find x when y = 42
1) Write equation:y = kx 36 = k(6)
36 = 6kk = 6, so y = 6x
2) Plug in given value, solve for missing! y = 6x
42 = 6x 7 = x