how do you find additional points on a line with a slope of 1/2 and a given point of (7,-2)?
To find additional points on a line with a given slope and a point, you can follow these steps:
1. Start with the given point and slope. In this case, the given point is (7, -2) and the slope is 1/2.
2. Use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
3. Substitute the values of the slope and the given point into the equation. y = (1/2)x + b
4. Solve for the y-intercept, b. Use the given point (7, -2) to substitute x and y into the equation, and solve for b. Plug in 7 for x and -2 for y:
-2 = (1/2)(7) + b
-2 = 7/2 + b
-2 - 7/2 = b
-4/2 - 7/2 = b
-11/2 = b
5. Write the equation of the line with the slope and y-intercept found. The equation is y = (1/2)x - 11/2.
6. Using the equation, substitute various values for x to find the corresponding y-values and get additional points on the line. For example, if you let x = 0, you can solve for y:
y = (1/2)(0) - 11/2
y = 0 - 11/2
y = -11/2
So, another point on the line is (0, -11/2).
You can repeat this step with different x-values to find more points on the line.