Find at least five ordered pair solutions and graph. -x+5...

Key Concepts

Linear Equations

A linear equation represents a straight line in the coordinate plane and is defined by variables that are all to the first power. The equation can be manipulated into a form such as slope-intercept form (y = mx + b), which directly shows its slope and y-intercept, making it easier to analyze and graph.

Ordered Pair Solutions

Ordered pair solutions are sets of two numbers, typically expressed as (x, y), that satisfy the given equation. For a linear equation, every ordered pair that lies on the line is a solution, and finding multiple ordered pairs can be done by substituting different values for one variable and solving for the other.

Slope-Intercept Form

The slope-intercept form of a linear equation, written as y = mx + b, explicitly shows the line's slope (m) and its y-intercept (b). This form is particularly helpful for graphing since it clearly indicates where the line crosses the y-axis and how steep the line is.

Graphing on a Coordinate Plane

Graphing on a coordinate plane involves plotting ordered pair solutions (points) on the grid and then drawing a line through these points. This visual representation helps in understanding the behavior of the equation and verifying the correctness of the ordered pair solutions.

Intercepts

Intercepts are points where the graph crosses the axes. In the context of linear equations, the y-intercept is found by setting x to zero, and the x-intercept is found by setting y to zero. These points provide a quick way to start plotting the line on a graph.

Transcript

00:01 We are going to find some ordered pairs that satisfy the equation negative x plus 5y equals 0, and then plot those on our graph.

00:11 So i'm starting with let x equals 0 in my x, y, ordered pair.

00:27 So we'll take our equation, and in place of x, we're going to let x equal 0.

00:37 Negative 0 is silly.

00:39 We don't need anything there.

00:41 So we end up with 5 y equals 0, divide both sides by 5, and we get y equals 0.

00:50 So our first point is 0 ,0.

00:52 We're going to plot it right there on our graph.

00:55 Okay.

00:58 And make my pin a little thinner.

01:00 I'm going to run out of room.

01:03 Okay, next we're going to let x equal 5.

01:06 Let's do that down here.

01:07 So we have negative 5.

01:09 So in place of x, i put 5 in parentheses, plus 5, y equals zero.

01:17 So i'm going to add five to both sides to solve for y.

01:21 I have five y equals five.

01:26 You divide both sides by five so y is one.

01:29 So when x is five, y is one.

01:31 Let's plot that.

01:32 We go five in the x direction and one up in the positive y direction.

01:39 Okay next we'll let x be 10.

01:42 So we have negative 10 plus 5y equals 0 add 10 to both sides we have 5 y equals 10 divide both sides by 5 we get y equals 2 so when x is 10 y is 2 so we're going to start at the origin go 10 in the positive x direction to the right.

02:10 Let's get my pointer...

Please give Ace some feedback