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Math  /  Geometry

QuestionFind the equation of the line that passes through the points (−8,10)(-8,10) and (4,1)(4,1).

Studdy Solution

STEP 1

1. We are finding the equation of a straight line.
2. The line passes through the points (−8,10)(-8, 10) and (4,1)(4, 1).

STEP 2

1. Calculate the slope of the line.
2. Use the point-slope form to find the equation of the line.
3. Simplify the equation to slope-intercept form.

STEP 3

Calculate the slope of the line using the formula:
m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (−8,10)(-8, 10) and (4,1)(4, 1):
m=1−104−(−8) m = \frac{1 - 10}{4 - (-8)} =−94+8 = \frac{-9}{4 + 8} =−912 = \frac{-9}{12} =−34 = -\frac{3}{4}

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)
Substitute the slope m=−34 m = -\frac{3}{4} and one of the points, say (−8,10)(-8, 10):
y−10=−34(x+8) y - 10 = -\frac{3}{4}(x + 8)

STEP 5

Simplify the equation to slope-intercept form y=mx+b y = mx + b :
Distribute the slope on the right side:
y−10=−34x−34×8 y - 10 = -\frac{3}{4}x - \frac{3}{4} \times 8 y−10=−34x−6 y - 10 = -\frac{3}{4}x - 6
Add 10 to both sides to solve for y y :
y=−34x−6+10 y = -\frac{3}{4}x - 6 + 10 y=−34x+4 y = -\frac{3}{4}x + 4
The equation of the line is:
y=−34x+4 \boxed{y = -\frac{3}{4}x + 4}

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