Slippery Slope
Find the slope of the line passing through the points (2, 3) and (5, 9)
m = 2
Convert y - 3 = 2(x - 1) to slope-intercept form
y = 2x + 1
Find x- and y-intercepts of y = 3x - 6.
x-intercept: (2, 0); y-intercept: (0, -6)
Solve by elimination:
2x + y = 5
x - y = 1
(2,1)
In the function y = 2x + 3, which is the independent variable (input) and which is the dependent variable (output)?
Independent (input): x
Dependent (output): y
What does a line with a slope of zero look like? Give an example equation.
Horizontal Line (y = c)
Write y = -4x + 7 in point-slope form using the point (0, 7).
y - 7 = -4(x - 0)
What does the y-intercept represent for a linear function?
Value of y when x = 0 (where line crosses y-axis)
What does it mean if a system is inconsistent?
No solution (parallel lines)
What does the slope, m, of a line, represent?
Change in y over change in x
or
rise (y) over run (x)
Find the slope of a line parallel to one passing through (-2, 3) and (5, -1).
m = -4/7
Convert 3x - 5y = 15 to point-slope form using its y-intercept.
y + 3 = (3/5)(x - 0)
For 4x + 3y = 12, find intercepts and a third point using slope.
x-intercept: (3, 0); y-intercept: (0, 4); third point: e.g., (1, 8/3)
Solve by substitution:
y = 2x - 3
3x + 4y = 7
(19/11, 5/11)
Write the general equation of a linear function in:
Slope-intercept form,
Point-slope form, and
Standard form
y = mx + b
(y-y1) = m(x-x1)
Ax + By = C
A line has an undefined slope. What does it look like? Give an example equation.
It is a vertical line (x = c)
A line with slope 2/3 passes through (1, -2). Write its equation in standard form
2x - 3y = 8
Graph y - 1 = 1/2(x + 2) mentally. Find intercepts and one other point.
x-intercept: (-4, 0); y-intercept: (0, 2); other point: e.g., (-2, 1)
Solve:
2x - 3y = 5
4x - 6y = 7
Is it consistent or inconsistent?
Inconsistent (parallel lines, no solution)
Define domain and range
What is the domain of the line y = -3x-5?
Domain: all the possible input (x) values
Range: all the possible output (y) values
Domain: all real numbers
What is the slope of the line perpendicular to
(y-2) = 4/5(x-1)?
m = -5/4
Convert y + 4 = -3/2(x - 2) to standard form, then find a point on the line when x = 4
3x + 2y = -2; point (4, -7)
For 2x - 5y = 10, find intercepts, graph, and determine the slope of a perpendicular line through (5, 0).
x-intercept: (5, 0); y-intercept: (0, -2); perpendicular slope: -5/2
Solve:
3x + 5y = 10
6x + 10y = 20
Find a third equation consistent with this dependent system.
Infinite solutions (dependent); e.g., 9x + 15y = 30
A tank loses 2 gallons/minute, with 50 gallons after 5 minutes. Find when it’s empty and the domain.
t = 30 minutes; domain: t ≥ 0