Three Forms of Linear Equations
What form is y = 4x - 3?
Slope-intercept form.
Is y = 5x - 4 linear or nonlinear?
Linear.
For y = -2x + 7, what is the slope and y-intercept?
Slope -2; y-intercept (0, 7).
Function A: y = 2x + 5. Function B: y = 4x + 1. Which has the greater rate of change?
Function B: 4 > 2.
Are y = 2x + 1 and 2x - y = -1 equivalent?
Yes. Both are y = 2x + 1.
Write y - 2 = 3(x - 1) in slope-intercept form.
y = 3x - 1
A table increases by 3 in y whenever x increases by 1. Linear or nonlinear?
Linear; the rate of change is constant.
Is y = 3x - 4 increasing, decreasing, or constant?
Increasing.
Function A: y = 3x + 7. Function B: y = 5x + 2. Which has the greater initial value?
Function A: 7 > 2.
Is (2, 7) a solution of y = 3x + 1?
Yes: 7 = 3(2) + 1.
Rewrite y = -2x + 5 in standard form.
2x + y = 5.
Is y = x² + 1 linear or nonlinear?
Nonlinear.
Find the x-intercept of y = 2x - 8.
(4, 0).
A table shows (0, 4), (1, 6), (2, 8). Write its linear function.
y = 2x + 4.
Convert y - 5 = -3(x + 2) to slope-intercept form.
y = -3x - 1.
Rewrite 3x + 2y = 12 in slope-intercept form.
y = -(3/2)x + 6.
A graph is a curved parabola. Is the function linear or nonlinear?
Nonlinear.
For y = -x + 3, what is the domain and range when x can be any real number?
Domain: all real numbers; range: all real numbers.
Function A: y = 3x + 2. Function B has points (0, 5), (2, 9). Compare their slopes and initial values.
A has greater slope (3 > 2); B has greater initial value (5 > 2).
Does (3, 2) lie on the graph of 2x + y = 8? Explain.
Yes: 2(3) + 2 = 8.
Write the equation of the line with slope -2 passing through (3, 4) in point-slope form.
y - 4 = -2(x - 3).
A table has x-values 0, 1, 2, 3 and y-values 2, 5, 8, 11. Is it linear? Write its equation.
Yes. y = 3x + 2.
For the linear function y= 2x-4, when is the function positive, and when is it negative?
Positive when x>2; negative when x<2. The function equals zero at x=2.
A taxi charges $4 to start and $2 per mile. Write a function for cost C after m miles, and interpret its slope and initial value.
C = 2m + 4; slope $2 per mile; initial value $4 starting fee.
Rewrite 4x - 2y = 10 as y = mx + b. State m and b.
y = 2x - 5; m = 2 and b = -5.