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Math  /  Algebra

QuestionQuestion Write the equation of the line that passes through the points (4,7)(4,7) and (5,−7)(5,-7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Studdy Solution

STEP 1

1. We are given two points: (4,7) (4,7) and (5,−7) (5,-7) .
2. We need to find the equation of the line passing through these points.
3. The equation should be in fully simplified point-slope form unless the line is vertical or horizontal.

STEP 2

1. Calculate the slope of the line.
2. Use the point-slope form of the equation of a line.
3. Simplify the equation if necessary.

STEP 3

Calculate the slope of the line using the formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (4,7)(4,7) and (5,−7)(5,-7):
m=−7−75−4=−141=−14 m = \frac{-7 - 7}{5 - 4} = \frac{-14}{1} = -14

STEP 4

Use the point-slope form of the equation of a line, which is:
y−y1=m(x−x1) y - y_1 = m(x - x_1)
Choose one of the given points, say (4,7)(4,7), and substitute m=−14 m = -14 :
y−7=−14(x−4) y - 7 = -14(x - 4)

STEP 5

Simplify the equation if necessary. In this case, the equation is already in point-slope form and does not require further simplification.
The equation of the line in point-slope form is:
y−7=−14(x−4) y - 7 = -14(x - 4)

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