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Math  /  Geometry

QuestionGraph the line. y−1=−32(x+5)y-1=-\frac{3}{2}(x+5)

Studdy Solution

STEP 1

1. The equation given is in point-slope form.
2. The goal is to graph the line represented by the equation.

STEP 2

1. Identify the point and slope from the point-slope form equation.
2. Convert the equation to slope-intercept form.
3. Plot the point on the graph.
4. Use the slope to determine another point.
5. Draw the line through the points.

STEP 3

Identify the point and slope from the point-slope form equation:
The equation is y−1=−32(x+5) y - 1 = -\frac{3}{2}(x + 5) .
- The point is (−5,1)(-5, 1). - The slope is −32-\frac{3}{2}.

STEP 4

Convert the equation to slope-intercept form y=mx+b y = mx + b .
Start with the given equation:
y−1=−32(x+5) y - 1 = -\frac{3}{2}(x + 5)
Distribute the slope on the right side:
y−1=−32x−32×5 y - 1 = -\frac{3}{2}x - \frac{3}{2} \times 5
y−1=−32x−152 y - 1 = -\frac{3}{2}x - \frac{15}{2}
Add 1 to both sides to solve for y y :
y=−32x−152+1 y = -\frac{3}{2}x - \frac{15}{2} + 1
Convert 1 to a fraction with a denominator of 2:
y=−32x−152+22 y = -\frac{3}{2}x - \frac{15}{2} + \frac{2}{2}
Combine the constants:
y=−32x−132 y = -\frac{3}{2}x - \frac{13}{2}

STEP 5

Plot the point (−5,1)(-5, 1) on the graph.

STEP 6

Use the slope −32-\frac{3}{2} to determine another point.
From (−5,1)(-5, 1), move down 3 units and right 2 units to find another point, (−3,−2)(-3, -2).

STEP 7

Draw the line through the points (−5,1)(-5, 1) and (−3,−2)(-3, -2).
The line is now graphed using the points and slope.

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