Answer:
To find the line through the point (-1, 2) with a slope of -3/4, we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1)
Where (x1, y1) represents the coordinates of the given point and m represents the slope of the line.
In this case, the given point is (-1, 2) and the slope is -3/4. Plugging these values into the point-slope form, we get:
y - 2 = (-3/4)(x - (-1))
Simplifying further:
y - 2 = (-3/4)(x + 1)
Now, let's expand the equation:
y - 2 = (-3/4)x - 3/4
To isolate y, we can add 2 to both sides of the equation:
y = (-3/4)x - 3/4 + 2
Simplifying further:
y = (-3/4)x + (8/4) - (3/4)
Combining like terms:
y = (-3/4)x + 5/4
Therefore, the equation of the line through the point (-1, 2) with a slope of -3/4 is y = (-3/4)x + 5/4.
Explanation: