Slope
A linear graph goes through points (-4,6) and (4,2). What is the slope of the graph?
-1/2
You rent a boat for a day. The flat charge is $25 with an additional $10 dollars for every hour you have it for. Write an equation in slope-intercept form for the total cost, y, after x hours of renting the boat.
y= 10x+25
What type of transformation keeps the graph the exact same but moves it to a different place?
A translation.
Rewrite the equation 3x+6y=21 so that it is in slope-intercept form.
y=-1/2x+3.5
What should you look for when comparing equations/graphs to see if lines are parallel?
The same slope.
Find the slope of a line that passes through points (2,4) and (-6,3).
1/8
Convert 9x+3y=24 into slope-intercept form.
y=3x+8
The parent function of a graph is f(x)=x
What does the equation look like after the graph has been horizontally shrunk by a scale factor of 3 and translated 2 units up?
g(x)=1/3(x+2)
Write y=3/5x+2 in point-slope form.
y-2=3/5(x-0)
y-2=3/5(x)
Line t has a slope of 2/3. Line m is perpendicular to line t. What is the slope of line m?
-3/2
What is the slope of the line -3x+5y=20?
3/5
The water level of a river is 28 feet. During a 5-hour-long rainstorm the level increases by 3 inches per hour. What is the water level at the end of the storm?
29 feet and 3 inches (29.25 feet)
Equation: y=5(1/4)+28
Rewrite the equation so that it is translated 4 units right with a horizontal stretch that has a scale factor of 2.
y=3x+5
y=1/2(3x-4)+5
A line passes through points (2,3) and (-7,5). Write an equation for this line in point-slope form.
y-2=-2/9(x-3) or y-5=-2/9(x+7)
Are lines y=2/3x+8 and -2x+3y=9 parallel or perpendicular?
Parallel; they have the same slope.
What is the slope of 15x+3y=9?
-5
The slope of a line is -1/4 and it goes through the point (8,3). What is the equation in slope-intercept form?
y=-1/4x+5
The parent function of a graph is f(x)=x2
The equation for a translated graph is g(x)=3(-x2)+5
What transformations occurred to the graph?
Vertical stretch, sf:3
Reflection over the x-axis
Vertical translation up 5 units
Convert y=3/4x-5 to standard form.
3x-4y=20
The equation for a line is y=1/3x-4
Is the line 3x-y=9 parallel, perpendicular, or neither?
Perpendicular; when solved for slope-intercept form, the equation is y=-3x-9, which has an opposite reciprocal slope to the first equation, making it perpendicular.