How do you graph the straight line equation, y=9-2x?
Graph the line y=9-2x:
Since you know that the graph is a straight line you need only find two points that satisfy the equation and connect them with a line. From geometry you know that two points determine a line.(i.e. through two points there is one and only one line.)
But a slightly more efficient way is to write the equation in a recognizable form; here it is simplest to write in slope-intercept form or y=mx+b. m represents the slope while b represents the y-intercept (i.e. where the graph crosses the y-axis.)
y=9-2x becomes y=-2x+9. Thus the slope is -2: the graph falls from left to right, and every 1 unit you move to the right the graph falls two units. Also, the graph contains the point (0,9) as 9 is the y-intercept.
Some points on the line are (0,9), (1,7) (notice that as the x value increases by 1, the y value decreases by 2), (2,5),(3,3),(4,1), etc... You might check one of these points, say (3,3). Substituting 3 for x and 3 for y into the original equation we get 3=9-2(3) which is true.
In order to graph this equation, y=9-2x, you need to know the y-intercept and the slope and you will know by using the formula y=mx+b. m being the slope and b being the y-intercept. So let rearrange the formula to look a little bit more familiar: y=-2x+9. The slope is -2 and the y-intercept is 9. So in order to graph this you will plot a point at (0,9) and from this point you will down 2 and 1 over to the right since the slope is -2/1 which is rise over run. The red dot is the intercept and the green dots are a result of using rise over run (the gray lines) from the slope -2/1
Well, first you could rearrange this equation so that it says y=-2x+9. This helps to show you that the slope is -2 and that the y-intercept is 9. This tells you that the line will be going downward and that it will intercept the y-axis at nine.
Now, you can start from that 9 on the y-axis and go down one, right two. This is because the fraction form of -2 is -2/1, so you do the previous step while going downward to get the negative slope.
You keep doing this until you want your graph to end, and then for the left side of the graph, you would do the same thing but instead of going right, you are going left. And also you are going up instead of down.