this other one how can i actually prove it if this is the equation to use.
the problem states:
Prove that if a line has slope ma nd y-intercept b, then an equation of th eline is y=mx+b. then it says (Hint: use the point-slope equation theorem)
I've looked at it but i understand it but i don't know what to answer for this problem.
To prove that the equation of a line with slope m and y-intercept b is y = mx + b, you can use the point-slope equation theorem. Here is how you can approach the problem:
1. Start by recalling the point-slope equation theorem, which states that the equation of a line passing through the point (x1, y1) with slope m is given by: y - y1 = m(x - x1).
2. Let's assume that the line you are trying to prove has a slope of m and a y-intercept of b.
3. Since the y-intercept is the point where the line intersects the y-axis, it will have a corresponding x-coordinate of 0. Therefore, you can choose a point on the line as (0, b).
4. Now, substitute the values of the slope (m), the point (0, b), and the corresponding coordinates (x1 = 0 and y1 = b) into the point-slope equation: y - b = m(x - 0).
5. Simplify the equation further by removing the parentheses: y - b = mx.
6. Finally, add b to both sides of the equation to isolate y: y = mx + b.
7. You have now obtained the equation y = mx + b, which matches the equation you were asked to prove.
By following these steps and utilizing the point-slope equation theorem, you were able to prove that if a line has a slope m and y-intercept b, then the equation of the line is indeed y = mx + b.