Final answer:
The value of A is 6.8 for the line with a slope of -5/4 that passes through the points (2, -1) and (A, -7), by using the slope formula and algebraic manipulation.
Step-by-step explanation:
To find the value of A for the line with a slope of -5/4 that passes through the points (2, -1) and (A, −7), we can use the slope formula which is (change in y) / (change in x) = slope, or (y2 - y1) / (x2 - x1). In this case, we have the two points (2, -1) and (A, −7).
To solve for A, the equation will be:
1. Substitute the known values into the slope formula: (-7 - (-1)) / (A - 2) = -5/4.
2. Simplify the numerator: (-7 + 1) / (A - 2) = -5/4.
3. Now, solve for A: (-6) / (A - 2) = -5/4.
4. Cross-multiply to get 4(-6) = -5(A - 2).
5. Solve the equation: -24 = -5A + 10.
6. Add 5A to both sides: -24 + 5A = 10.
7. Subtract 10 from both sides: 5A = 34.
8. Finally, divide by 5: A = 34/5.
9. The value of A is 6.8.
Therefore, the line with a slope of -5/4 passing through the points (2, -1) and (A, −7) will have the point A equal to 6.8.