Final answer:
To represent State Road 7 (441) in slope-intercept form and standard form, we can use the perpendicular nature of Okeechobee Boulevard and State Road 7 (441). By finding the slope of Okeechobee Boulevard and using its negative reciprocal as the slope of State Road 7 (441), we can create the equation. Using the given point (4,3) and the slope, we can find the y-intercept and write the equation in slope-intercept form as y = (7/3)x - 11/3 and in standard form as 7x - 3y = 11.
Step-by-step explanation:
To create an equation that represents State Road 7 (441), we need to find the equation in slope-intercept form (y = mx + b) or standard form (Ax + By = C). Since Okeechobee Boulevard and State Road 7 (441) are perpendicular, the slope of State Road 7 (441) will be the negative reciprocal of the slope of Okeechobee Boulevard.
The slope of Okeechobee Boulevard can be found by rearranging the equation 3x - 7y = 10 to y = mx + b form. We subtract 3x from both sides, and then divide by -7 to isolate the y variable. This gives us y = (-3/7)x + (10/7).
The slope of State Road 7 (441) is the negative reciprocal of -3/7, which is 7/3. To find the equation in slope-intercept form, we can substitute the slope (7/3) and the point (4,3) into the equation y = mx + b and solve for b. Plugging in the values, we get 3 = (7/3)(4) + b. Simplifying, we find b = -11/3.
Therefore, the equation to represent State Road 7 (441) in slope-intercept form is y = (7/3)x - 11/3, and in standard form is 7x - 3y = 11.