Question

Kyle and Luna are finding the value of a so the line passes through (-2,8) and (10,a) has a slope of 1/4. Is either of them correct?

Answer 1

To find the value of 'a' so that the slope of the line through (-2,8) and (10,a) is 1/4, we use the slope formula and solve for 'a', which results in 'a' being 11.

Step-by-step explanation:

The student is asking for the value of a so that the line passing through the points (-2,8) and (10,a) has a slope of 1/4. To find a, we can use the formula for the slope of a line, which is (y2 - y1) / (x2 - x1). We know the slope is 1/4, and we can plug in the coordinates (-2,8) and (10,a) into the formula. So, we have:

1. (a - 8) / (10 - (-2)) = 1/4,
2. (a - 8) / 12 = 1/4,
3. Cross multiplying gives us 4(a - 8) = 12,
4. 4a - 32 = 12,
5. 4a = 12 + 32,
6. 4a = 44,
7. a = 44 / 4,
8. a = 11.

Thus, for the slope to be 1/4, the value of a must be 11.