Answer:To write the equation of a line in standard form that passes through the point (8, 7.5) and has a slope of 3/4, we can use the point-slope form of a linear equation.
1) Start with the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) represents the given point and m represents the slope.
2) Substitute the values into the equation:
y - 7.5 = (3/4)(x - 8)
3) Simplify the equation:
y - 7.5 = (3/4)x - 6
4) Move the constant term to the other side of the equation:
y = (3/4)x - 6 + 7.5
5) Combine like terms:
y = (3/4)x + 1.5
6) To convert the equation to standard form, we multiply all the terms by 4 to eliminate fractions:
4y = 3x + 6
7) Rearrange the equation so that the x and y terms are on the same side and the constant term is on the other side:
-3x + 4y = 6
Therefore, the equation of the line in standard form that passes through the point (8, 7.5) with a slope of 3/4 is -3x + 4y = 6.
Explanation: