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Math  /  Geometry

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What is an equation of the line that passes through the points (4,8)(4,8) and (−2,−7)(-2,-7) ?
Answer Attemptiout of 2 □\square Stlunit Answer

Studdy Solution

STEP 1

1. We are given two points: (4,8) (4, 8) and (−2,−7) (-2, -7) .
2. We need to find the equation of the line that passes through these points.
3. The equation of a line can be expressed in the slope-intercept form y=mx+b y = mx + b .

STEP 2

1. Calculate the slope of the line.
2. Use the slope and one point to find the y-intercept.
3. Write the equation of the line.

STEP 3

Calculate the slope m m of the line using the formula:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (x1,y1)=(4,8) (x_1, y_1) = (4, 8) and (x2,y2)=(−2,−7) (x_2, y_2) = (-2, -7) :
m=−7−8−2−4 m = \frac{-7 - 8}{-2 - 4} m=−15−6 m = \frac{-15}{-6} m=52 m = \frac{5}{2}

STEP 4

Use the slope m=52 m = \frac{5}{2} and one point, say (4,8) (4, 8) , to find the y-intercept b b using the formula:
y=mx+b y = mx + b
Substitute the values:
8=52×4+b 8 = \frac{5}{2} \times 4 + b 8=10+b 8 = 10 + b b=8−10 b = 8 - 10 b=−2 b = -2

STEP 5

Write the equation of the line using the slope m=52 m = \frac{5}{2} and y-intercept b=−2 b = -2 :
y=52x−2 y = \frac{5}{2}x - 2
The equation of the line is:
y=52x−2 \boxed{y = \frac{5}{2}x - 2}

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