The graph of the equation y = −2x + 3 is shown. Which statement is true about every point on the graph?
A. The x-coordinate and the y-coordinate have different signs.
B. The y-coordinate is less than the x-coordinate.
C. The y-coordinate is double the x-coordinate.
D. If you multiply the x-coordinate by -2 and then add 3, you get the y-coordinate.------
A little help? i think it's D but im not too sure.
go with it ...
Well, I have to "hand" it to you, you're on the right track! The equation given is in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -2 and the y-intercept is 3.
Since the slope is -2, it means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 2.
So when you multiply the x-coordinate by -2 (which is the same as a decrease of 2 in the x-coordinate) and then add 3, you should get the y-coordinate.
Therefore, I "count" on D being the correct answer!
Yes, you are correct! Statement D is true for every point on the graph.
The equation of the graph is y = -2x + 3. This means that for any point on the graph, the y-coordinate can be found by multiplying the x-coordinate by -2 and then adding 3.
For example, let's consider a point on the graph with coordinates (1, 1). Plugging this into the equation:
y = -2x + 3
1 = -2(1) + 3
1 = -2 + 3
1 = 1
As we can see, the y-coordinate does indeed equal -2 times the x-coordinate plus 3. This pattern holds true for every point on the graph, which means Statement D is correct.
To determine which statement is true about every point on the graph of the equation y = -2x + 3, we can analyze the equation and the options provided.
The given equation is in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this case, the slope is -2 and the y-intercept is 3.
Option D states: "If you multiply the x-coordinate by -2 and then add 3, you get the y-coordinate."
To confirm if this statement is true, we can substitute any point on the graph into the equation and see if it holds.
Let's choose a point on the graph, such as (1, 1):
-2 * (1) + 3 = -2 + 3 = 1
Since -2 multiplied by 1, plus 3, does indeed give us 1 (the y-coordinate), Option D is true for every point on the graph. Therefore, the correct answer is D.