Features of :linear functions (slope & intercepts)
What is the slope and y- intercept of y= 2x +3
Slope: 2
y- intercept: (0,3)
Write the equation of the line with slope 3 and y-intercept -2
y= 3x - 2
Solve: 2x + 5=11
x=3
What mistake is made if someone solves 7x=2 as x =27
What is the domain and range of y = 2x +3
Domain: (-inf, inf)
Range: (-inf, inf)
Find the x and y intercept of y = -3x + 6
y- intercept: (0,6)
x- intercept: (2,0)
Find the equation of the line through (0,-3) and (4,1).
y= x - 3
Solve: 5x - 7 =18
x = 5
A student writes 2(x+ 3) as 2x + 3, what is wrong?
Incorrect distribution; it should be 2x + 6
What is the domain and range of y= 5
Domain: (-inf, inf)
Range: y = 5
Rewrite 4x + 2y = 10 in slope- intercept form and state the slope and intercepts
y = -2x + 5
Slope: -2
y- intercept: (0,5)
x- intercept: (5/2,0)
Find the equation of the line through (2,6) and (-2,4).
y = 1/2x + 5
Solve: 3(2x + 5) - 2(2x -3) = 12
x= -9/2
A student combines 3x - 4x as 7x. What is the mistake?
Wrong sign; correct is -x
What is the domain and range of y = x2
Domain: (-inf, inf)
Range: 0 ≤ y < inf OR [0, inf)
Find the slope and both intercepts of 3x + 4y = 12
Slope: -3/4
y-intercept: (0,3)
x-intercept: (4,0)
Find the equation of the line through (-1,2) and (2,-4).
y = -2x
Solve: 4x - 3(x-2) = 2x + 5
x = 1
A student solves 3x + 2 - 2(2x-3) = 13 as 7x =2. What's their main error?
Mis-distributed -2(2x-3)
What is the domain and range of y = (x-2)2+ 1
Domain: [0, inf) OR 0 ≤ x < inf
Range: [1,inf) OR 1 ≤ y < inf
A line passes through (0,7) and has slope -1/2. What is the x-intercept?
(14,0)
Write the equation of the line through (3,-2) and (3,5).
x=3 (vertical line)
Solve: 5(x - 1) + 2 = 3x +4
x = 7/2
Rewrite a short "note to the author" explaining how to avoid mistakes when distributing and combining like terms.
Always use parentheses, distribute carefully to each term, and combine only like terms. Double-check by plugging your answer back into the equation.
What is the domain and range of y = sqrt(x+4)
Domain: [-4, inf) OR -4 ≤ x < inf
Range: [0 , inf) OR 0≤ y < inf