Remediation

Slope

 Find the slope of a line given two points: (3, 4) and (7, 8).  m = (8 – 4)/(7 – 3) = 4/4 = 1  The slope is 1.

Y-intercept  The y-intercept is where the line crosses the y axis.  It is written (0, #) since the x part of the point is 0 when it goes across the y axis.  To find the y-intercept in a line, put in 0 for x and solve for y.

Y-intercept  Given the line y = 2x + 5, find the y intercept.  First substitute in 0 in place of x.  y = 2(0) + 5  Now solve for y  y=5  This the y-intercept. (0, 5)

X-intercept  The x-intercept is where the line crosses the x axis.  It is written (#, 0) since the y part of the point is 0 when it goes across the x axis.  To find the x-intercept in a line, put in 0 for y and solve for x.

X-intercept  Given the line y = 2x + 5, find the x intercept.  First substitute in 0 in place of y.  0 = 2x + 5  Now solve for x  -5 = 2x  -5/2 = x  This the x-intercept. (-5/2, 0)

Assignment: Find the slope of the line that passes through the points: 1)(-5, 3) and (0, 0) 2)(-3, 7) and (5, -3) 3)(-3, 8) and (-3, -4) 4)(13.5, 6) and (-11, 6) Click on picture for examples worked out Image from: //upload.wikimedia.org/wikipedia/commons/c/ce/ChilkootPass_Slope.jpg

Assignment, continued Find the equation of the line that passes through: 5) (6, 4) and m = 6) (-2, 7) and m = Start with y=mx + b

Assignment, continued Find the equation of the line that passes through the points: 7) (-8, -6) and (0, -6) 8) (1, -6) and (7, -4) 9) (-8, 3) and (0, 0) 10) (17.5, -9) and (17.5, 13) Click on picture for examples worked out Image from:

Graphing Lines  When a line is in slope intercept form, y=mx + b, you can graph by using the slope and the intercept.  Start by labeling your m (slope) and b (y- intercept).  Plot the b and move (rise/run) for the slope.

Rise Run Graphing Lines y= 2x + 4

Examples  A 6-inch scented candle burns at a rate of 0.1 inches each hour.  Starting at 6 inches= y-intercept, Decrease 0.1= slope -0.1  Let x=hours that the candle burns, y=height of the candle  *EQ: y=-0.1x+6 *Notice that the slope is negative because the candle height is decreasing as it burns!  *Q: How many hours has the candle burned if it is now 3.4 inches tall?  A: Use y=3.4, so 3.4=-0.1x =-0.1x, so x = 26 hours the candle burned  A national park has 8000 deer. It is estimated that the deer population will increase by 70 deer each year thereafter.  Starting 8000 = y-intercept, Increase 70 = slope  Let x=years from now, y=total deer in park  *EQ: y=70x+8000  *Q: How many deer will be in the park in 5 years?  A:Use x=5, so y=70(5)+8000=8350 deer in 5 years

Find the intercepts (page will check your answers) Interactive Slope Slider Slope Quiz Practice

Remediation Links Overview Slope Point-Slope Form Slope-Intercept Form