Plot the following coordinates in a graph and draw a straight line that covers all three dots. (0,-2),(1,-4),(2,-6) a. What is the y value of the line when x=6?
To plot the given coordinates, we'll use a Cartesian coordinate system:
First, plot the point (0, -2) on the graph. This is located at the y-axis (vertical line) when x=0, and it is 2 units down from the origin.
Next, plot the point (1, -4) on the graph. This is located at the x-axis (horizontal line) when x=1, and it is 4 units down from the origin.
Lastly, plot the point (2, -6) on the graph. This is located at the x-axis (horizontal line) when x=2, and it is 6 units down from the origin.
Now, draw a straight line that covers all three dots. This line will have a negative slope since the y-values decrease as x increases.
To find the equation of this line, we can calculate the slope using two points on the line, such as (0, -2) and (2, -6).
Slope (m) = (change in y) / (change in x)
= (-6 - (-2)) / (2 - 0)
= -4 / 2
= -2
The equation of a straight line (in slope-intercept form) is y = mx + b, where m is the slope and b is the y-intercept.
Using the slope (-2) and the point (0, -2) (which is on the line), we can plug these values into the equation and solve for b:
-2 = -2(0) + b
b = -2
Therefore, the equation of the line is y = -2x - 2.
To find the y value of the line when x=6, simply substitute x=6 into the equation and solve for y:
y = -2(6) - 2
y = -12 - 2
y = -14
So, the y value of the line when x = 6 is -14.