how do i write an equation in point slope form when the slope= -1/2 and it passes through (5,-8) and then how do i write an equation for the line in slope-intercept form? thanks
slope point is y-y1=m(x-x1)
slope intercept is y=mx+b
slope point: y+8=-1/2(x-5)
solving gives us the slope intercept form of y=-1/2x-11/2
thanks :)
wouldnt it be -1/2x + 11/2 because negative 1/2 times a negative 5 would be 11/2...i think
no because -1/2*-5= 5/2-8=-11/2
sorry your right i wrote something wrong down :)
To write an equation in point-slope form when given the slope and a point, follow these steps:
Step 1: Use the slope-intercept form, y - y₁ = m(x - x₁).
Step 2: Substitute the given values into the equation:
- Substitute the slope, m = -1/2.
- Substitute the coordinates of the given point (x₁, y₁) = (5, -8).
Step 3: Simplify the equation to point-slope form.
Now let's go through the steps in detail:
Step 1: Start with the slope-intercept form, y - y₁ = m(x - x₁).
Step 2: Substitute the given values:
- The slope, m = -1/2. Substitute it into the equation: y - y₁ = -1/2(x - x₁).
- The coordinates of the given point are (x₁, y₁) = (5, -8). Substitute these into the equation: y - (-8) = -1/2(x - 5).
Step 3: Simplify the equation to point-slope form:
- Simplify the left side by removing the parentheses: y + 8 = -1/2(x - 5).
- Distribute -1/2 to the terms inside the parentheses: y + 8 = -1/2x + 5/2.
- Move the constant term to the right side of the equation by subtracting 8 from both sides: y = -1/2x + 5/2 - 8.
- Simplify the right side: y = -1/2x - 11/2.
Now you have the equation in point-slope form: y = -1/2x - 11/2.
To convert this equation to slope-intercept form, follow these steps:
Step 1: Start with the point-slope form equation: y = -1/2x - 11/2.
Step 2: Simplify the right side of the equation to obtain the slope-intercept form (y = mx + b).
- The coefficient of x in the equation, -1/2, is equivalent to the slope, m.
- The constant term on the right side, -11/2, is equivalent to the y-intercept, b.
Therefore, the equation in slope-intercept form is: y = -1/2x - 11/2.
I hope this helps! Let me know if you have any other questions.