Final answer:
Without a second point or the slope, we cannot find the equation for a line through (6,4) directly. A line with a slope of 3 and y-intercept of 9 is given as an example in slope-intercept form, y = 3x + 9, which can then be converted into standard form as 3x - y = -9.
Step-by-step explanation:
To write the equation of a line passing through the point (6,4) in standard form, we first need to find the slope (m) and the y-intercept (b). Since we do not have a second point or the slope directly provided, we cannot find the equation using just the point (6,4). However, using the information given in the different figures provided, we can illustrate how one would normally calculate the slope-intercept form and convert it to standard form.
For a generic example based on the figures, a line with a slope of 3 and y-intercept of 9 would have the slope-intercept form y = mx + b, which is y = 3x + 9. To convert this to standard form, we would rearrange the terms to get the x and y on the same side, resulting in 3x - y = -9. Typically, the standard form of a line is ax + by = c, where a, b, and c are integers and a is non-negative.