Question

Write y-2=-1/2(x-4) in standard form and slope intercept form.

Standard form:_________________
Slope intercept form:________________

Answer 1

The slope-intercept form of the equation y - 2 = -1/2(x - 4) is y = -1/2x + 4, and its standard form is x + 2y = 8. These transformations involve solving for y and rearranging the equation to fit the required formats.

Step-by-step explanation:

To convert the equation y - 2 = -1/2(x - 4) into standard form and slope-intercept form, let's start with the slope-intercept form since it's more straightforward.

First, we solve for y to get the slope-intercept form:

1. Add 2 to each side of the equation:
2. y = -1/2(x - 4) + 2
3. Distribute the fraction and simplify:
4. y = -1/2x + 2 + 4\2
5. Combine like terms:
6. y = -1/2x + 4

The slope-intercept form of the equation is y = -1/2x + 4, where the slope (m) is -1/2, and the y-intercept (b) is 4.

Now, to place the equation in standard form, the general form is Ax + By = C, where A, B, and C are integers:

1. Multiply both sides by 2 to clear the fraction:
2. 2y = -x + 8
3. Move all variables to one side of the equation:
4. x + 2y = 8

The standard form of the equation is x + 2y = 8.