how do you find additional points on a line with a slope of 1/2 and a given point of (7,-2)?
need the points not the equation
slope means rise over run
so your slope is 1/2, meaning for every increase of 2 in the x, the y changes by 1
so keep adding 2 to the x, and 1 to the y to get as many extra points as you want without finding the equation
first extra point is (9,-1), then (11,0) etc
you could also subtract 2 from the x and subtract 1 from the y, e.g. (5,-3)
notice finding the slope between any pair will give you 1/2
umhh
did you see any equation in my answer?
I gave you points, not the equation.
To find additional points on a line with a given slope and a single point, you can use the slope-intercept form of a linear equation, which is:
y = mx + b
Where:
- y and x represent the coordinates of any point on the line.
- m represents the slope of the line.
- b represents the y-intercept of the line.
Given that the slope (m) is 1/2 and the given point is (7,-2), we can substitute these values into the equation:
-2 = (1/2) * 7 + b
To solve for b, we can rearrange the equation:
-2 - (1/2) * 7 = b
-2 - 7/2 = b
-4/2 - 7/2 = b
-11/2 = b
Now that we have the value of b, we can rewrite the equation of the line:
y = (1/2)x - 11/2
Now, if we substitute different values for x into this equation, we can calculate the corresponding y-values to get additional points on the line. For instance, if we choose x = 0:
y = (1/2) * 0 - 11/2
y = -11/2
Therefore, when x = 0, y = -11/2, giving us the point (0, -11/2) as an additional point on the line.