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Math  /  Algebra

QuestionA line passes through the point (−4,−3)(-4,-3) and has a slope of 32\frac{3}{2}. Write an equation in slope-intercept form for this line.

Studdy Solution

STEP 1

1. The line passes through the point (−4,−3)(-4, -3).
2. The slope of the line is 32\frac{3}{2}.
3. We need to write the equation of the line in slope-intercept form, which is y=mx+by = mx + b.

STEP 2

1. Understand the slope-intercept form.
2. Substitute the slope into the equation.
3. Use the given point to find the y-intercept.
4. Write the final equation.

STEP 3

Understand the slope-intercept form. The slope-intercept form of a line is given by:
y=mx+b y = mx + b
where m m is the slope and b b is the y-intercept.

STEP 4

Substitute the slope into the equation. Given that the slope m=32 m = \frac{3}{2} , we substitute it into the slope-intercept form:
y=32x+b y = \frac{3}{2}x + b

STEP 5

Use the given point (−4,−3)(-4, -3) to find the y-intercept b b . Substitute x=−4 x = -4 and y=−3 y = -3 into the equation:
−3=32(−4)+b -3 = \frac{3}{2}(-4) + b
Simplify and solve for b b :
−3=−6+b -3 = -6 + b
Add 6 to both sides to solve for b b :
b=−3+6 b = -3 + 6 b=3 b = 3

STEP 6

Write the final equation using the slope and y-intercept. Substitute m=32 m = \frac{3}{2} and b=3 b = 3 into the slope-intercept form:
y=32x+3 y = \frac{3}{2}x + 3
This is the equation of the line in slope-intercept form.

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