Final answer:
To find the equation of the line that passes through (2,-4) with a slope of 1/2, first use the slope-intercept form y = mx + b to find b, making it y = (1/2)x - 5, and then rearrange into standard form: x - 2y = 10.
Step-by-step explanation:
The equation in standard form of the line that passes through the point (2,-4) and has a slope of 1/2 can be found using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. We can first plug the known slope and point into the equation: -4 = (1/2)(2) + b, which simplifies to -4 = 1 + b. Solving for b gives us b = -5. Therefore, the slope-intercept form of the line is y = (1/2)x - 5. To convert this to standard form, which is Ax + By = C, we can multiply the entire equation by 2 to get rid of the fraction: 2y = x - 10. Rearranging the terms gives us the standard form x - 2y = 10.