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Math  /  Algebra

QuestionUse point-slope form to write the equation of a line that passes through the point left parenthesis, 18, comma, 20, right parenthesis (with slope minus, start fraction, 3, divided by, 2, end fraction

Studdy Solution

STEP 1

1. We are given a point (18,20)(18, 20) through which the line passes.
2. The slope of the line is −32-\frac{3}{2}.
3. We need to use the point-slope form to write the equation of the line.

STEP 2

1. Recall the point-slope form of a line.
2. Substitute the given point and slope into the point-slope form.
3. Simplify the equation if necessary.

STEP 3

Recall the point-slope form of a line. The point-slope form is given by:
y−y1=m(x−x1) y - y_1 = m(x - x_1)
where (x1,y1) (x_1, y_1) is a point on the line and m m is the slope.

STEP 4

Substitute the given point (18,20)(18, 20) and slope −32-\frac{3}{2} into the point-slope form.
Given: x1=18 x_1 = 18 y1=20 y_1 = 20 m=−32 m = -\frac{3}{2}
Substitute these values into the equation:
y−20=−32(x−18) y - 20 = -\frac{3}{2}(x - 18)

STEP 5

Simplify the equation if necessary. In this case, the equation is already in point-slope form, so no further simplification is needed unless a different form is required.
The equation of the line in point-slope form is:
y−20=−32(x−18) y - 20 = -\frac{3}{2}(x - 18)

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