Slope Intercept Form
What is the equation for slope-intercept form? What does each letter stand for?
(x,y) are a point on the line
m is the slope
b is the y-intercept
What is the formula for point-slope form?
y = y1 = m(x - x1)
What types of slopes do parallel lines have?
(Same, equal)
Negative reciprocal slopes
These slopes multiply to - 1
Write an equation in slope-intercept form with the slope of 2 and y-intercept (0, -3)
y = 2x - 3
Write the equation in point-slope form of a line with a slope of 3 and passing through the point (9, -2)
y + 2 = 3(x - 9)
3
Is it possible for two lines with negative slopes to be perpendicular?
A cell phone battery is at 20% and is charging at a rate of 12% per hour.
Write an equation in slope-intercept form that gives the battery percentage y after x hours.
y=12x+20
A hiking trail climbs steadily. After walking 2 miles, the elevation is 900 ft. After walking 5 miles, the elevation is 1,200 ft.
Write an equation in point-slope form relating elevation y to distance walked x.
y−900=100(x−2)
What would be the slope of a line that is parallel to a line that passes through the points (-1, -2) and (-3, -1)?
1/2
Are the lines perpendicular or not?
L1: (0 , 3) , (3 , 1)
L2: (-1 , 4) , (-7 , -5)
Yes
A taxi charges a $4 starting fee plus $2.30 per mile.
Write an equation in slope-intercept form for the cost y after x miles.
y=2.30x+4
Write the equation of a line in point-slope form that passes through the points (3, 2) and (9, 3)
y - 3 = 1/6(x - 9)
or
y - 2 = 1/6(x - 3)
What is the equation of a line that is parallel to y - 1 = 8 (x + 1) and passes through (0,0)?
y = 8x
What is the slope of a line perpendicular to the line y +2 = 9 (x + 3)?
- 1/9
A skateboard ramp begins at ground level and rises at a rate of 3 feet for every 6 horizontal feet.
Write an equation in slope-intercept form for the height y (in feet) after x horizontal feet, assuming it starts at height 0.
y=1/2x
The temperature at noon is 68°F. One hour later it’s 74°F.
Write an equation in point-slope form for the temperature y (in °F) after x hours past noon.
y−68=6(x−0)
What is the equation of a line that is parallel to the line y -10 = 8 (x + 1) and passes through the point given in the point-slope form equation?
The same line!
y -10 = 8 (x + 1)
What is the equation of a line that is perpendicular to the line y = - 1/2 x + 3 and passes through the point (2, 4)?
y = 2x + 6