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Math  /  Algebra

Question2. Write the equation of the line with a slope of -3 and goes through the points (5,−6)(5,-6). The graph is optional, but provided if you prefer to use it.
Equation: y=−3xty=-3 x t Rises Run 6

Studdy Solution

STEP 1

1. The line has a slope m=−3 m = -3 .
2. The line passes through the point (5,−6) (5, -6) .
3. We are using the point-slope form of a linear equation to find the equation of the line.

STEP 2

1. Understand the point-slope form of a linear equation.
2. Substitute the given slope and point into the point-slope form.
3. Simplify the equation to the slope-intercept form, if necessary.

STEP 3

The point-slope form of a linear equation is given by:
y−y1=m(x−x1) y - y_1 = m(x - x_1)
where m m is the slope and (x1,y1) (x_1, y_1) is a point on the line.

STEP 4

Substitute the given slope m=−3 m = -3 and the point (5,−6) (5, -6) into the point-slope form:
y−(−6)=−3(x−5) y - (-6) = -3(x - 5)
This simplifies to:
y+6=−3(x−5) y + 6 = -3(x - 5)

STEP 5

Distribute the slope on the right-hand side:
y+6=−3x+15 y + 6 = -3x + 15
Subtract 6 from both sides to solve for y y :
y=−3x+15−6 y = -3x + 15 - 6
Simplify the equation:
y=−3x+9 y = -3x + 9
This is the equation of the line in slope-intercept form.

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