Coordinate Geometry Flashcards
Linear equation
y = mx + b, where m is the slope and b is the y-intercept. This is called slope-intercept form.
Slope
m = rise/run = (y2 - y1)/(x2-x1), where x1≠x2. Horizontal line has m=0, equation y=b. Vertical line has undefined slope equation x=a.
y- and x-intercept (linear)
To find the y-intercept plug in zero for x and solve for y. To find the x-intercept, plug in zero for y and solve for x.
Perpendicular and Parallel lines
The slopes of two lines which are perpendicular to each other are in the ratio of x : -1/x, where x is the slope of one of the lines (think: negative reciprocal). Parallel lines have equal slopes.
y=x line of symmetry (m=1, passes through origin)
interchanging x and y in an equation of any graph yields another graph that’s a reflection of original about the line y=x. Ex. y=2x+5 and y=(1/2)x-5
Solution of systems of linear equations and inequalities
Solution of 2 linear eq is point where lines intersect. Solution of 2 inequalities is all points that lie in intersection.
Distance formula
To find distance btwn (x1,y1) and (x2,y2): √((x2-x1)^2 + (y2-y1)^2)
Quadratic equation
y = ax^2 + bx + c, where a,b,c are constants and a≠0. The graph is a symmetrical shape called a parabola, which open upwards if a > 0 and down if a < 0. x-intercepts are the solution set.
y- and x-intercept (quadratic)
x-intercept can be found by solving quadratic formula set to 0. y-intercept is point on parabola at which x=0.
Quadratic formula
If ax^2 + bx + c = 0, and a is not 0, then x = (-b ± √(b^2 - 4ac))/2a
Circle graph
(x-a)^2 + (x-b)^2 = r^2, with center is at point (a,b) and with radius r
General rules of movement of graphs
If h(x)+c, shift h(x) upward by c units. If h(x)-c, shift downward. If h(x+c), shift to the left. If h(x-c), shift to the right. If ch(x), stretch h(x) vertically by factor of c if c>1 but shrink if 0<1.
Reflection about x-axis
graph of y = - h(x) is reflection of graph of y = h(x) about the x-axis
