Final answer:
To find a linear function that is perpendicular to 4x + y = 2 and passes through the point (-8, 3), we determine the slope of the given equation, find the negative reciprocal of that slope, and then use the point-slope form of a linear equation.
Step-by-step explanation:
To find a linear function that is perpendicular to the given equation and passes through the point (-8, 3), we need to determine the slope of the given equation and then find the negative reciprocal of that slope. The given equation is 4x + y = 2, and we can rewrite it in the slope-intercept form y = mx + b by isolating y. Subtracting 4x from both sides, we get y = -4x + 2. Therefore, the slope of the given equation is -4. The negative reciprocal of -4 is 1/4. So, the slope of the perpendicular line would be 1/4. Now we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values (-8, 3) and 1/4, we get y - 3 = 1/4(x + 8). Simplifying this equation, we have y - 3 = 1/4x + 2. Rearranging it to match the standard form, we get y = 1/4x + 5.