Presentation on theme: "Identify and Graph Linear Equations Name and Graph X and Y Intercepts"— Presentation transcript:
1Identify and Graph Linear Equations Name and Graph X and Y Intercepts Linear FunctionsIdentify and Graph Linear EquationsName and Graph X and Y Intercepts
2Vocabulary for this lesson Linear Equation – the equation of a line whose graph is a straight line.Standard Form – Linear equations written in the form Ax + By + C= 0X-Intercept – the point where a graphed line crosses the x-axis.Y-Intercept – the point where a graphed line crosses the y-axis.
3Determine whether each equation is linear… Determine whether each equation is linear….if so, write it in Standard FormCan it be written in standard form? Ax + By = C1) y = 5 – 2xYes+2x x2x + y = 52) y = -3 – xYes+ x xx + y = -33) 2xy – 5y = 6NoWhy?....The first term has TWO variables.
4Another way to look at this..... (3)(3)4) 1/3 y = -1Yesy = -3Can it be written in standard form? Ax + By = C5) 5x + 3y = z + 2NoWhy?....It has an extra variable “z”.6) y = x2 – 8NoWhy?....Because the “x” is squared.Another way to look at this.....To be considered LINEAR, an equation must have a degree of ONE.
5x and y - Intercepts To find the x-intercept, let y = 0 To find the y-intercept, let x = 0The x-int. is 7, so the graph intersects the x-axis at (7, 0)The y-int. is -2, so the graph intersects the y-axis at (0, -2)
6You can also graph using the intercepts. x-intercept (7, 0)y-intercept (0, -2)Now, draw a line through the points.
7Find the x & y intercepts, then graph the equation. (-5, 0)(0, -5)
8Find the x & y intercepts, then graph the equation. (3, 0)0 + 2y = 92y = 9y = 4.5(0, 4.5)
9Determine the x & y intercepts of each linear function. 10)11)xy-3-1-2123y-int. = 3or (0, 3)x-int. = -4or (-4, 0)x-int = -2Or (-2, 0)y-int = 2Or (0, 2)
10Real World Examplesx-int. of 20 means that after 20 minutes, the temperature was 0°F.y-int. of -4 means that at 0 time (the beginning) the temperature was °Fx-int. = 20 or (20, 0)12) Determine the x & y interceptsand describe what the intercepts mean.y-int. = -4 or (0, -4)
11Real World ExamplesDetermine the x & y intercepts and describe what they mean.x-int. = -3 or (-3, 0)y-int. = or (0, 2.25)The x-int. doesn’t make sense here because it is negative.The y-int. represents the base fare, or cost at zero miles.
12Determine the Intercepts and explain each. 14) Draining a pool15) Position of a scuba diver.Time (h)Volume (g)10,0802864047200657608432010288014The x-int. shows that after 12 sec., the diver was at the surface (0 m). The y-int. shows that when he started (0 s) he was at -24m or 24m below sea level.Time (s)Depth (m)-243-186-129-612The x-int. shows that after 14 hours, the pool had 0 gallons, or it was completely drained. The y-int. shows that at 0 hours, when they began, it had 10,080 gallons in it.