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Math  /  Algebra

QuestionFind an equation of the line having the given slope and containing the given point. m=−5,(6,0)m=-5,(6,0)
The equation of the line is y=y= □\square (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)

Studdy Solution

STEP 1

1. We are given a slope m=−5 m = -5 and a point (6,0) (6, 0) through which the line passes.
2. We need to find the equation of the line in slope-intercept form, which is y=mx+b y = mx + b .
3. The point-slope form of a line, y−y1=m(x−x1) y - y_1 = m(x - x_1) , can be used to find the equation.

STEP 2

1. Identify the given information and the form of the equation needed.
2. Use the point-slope form to find the equation of the line.
3. Convert the equation to slope-intercept form.
4. Simplify the equation, if necessary.

STEP 3

Identify the given information: - Slope m=−5 m = -5 - Point (6,0) (6, 0)
We need to find the equation in slope-intercept form y=mx+b y = mx + b .

STEP 4

Use the point-slope form of the equation of a line:
y−y1=m(x−x1) y - y_1 = m(x - x_1)
Substitute m=−5 m = -5 , x1=6 x_1 = 6 , and y1=0 y_1 = 0 into the equation:
y−0=−5(x−6) y - 0 = -5(x - 6)

STEP 5

Simplify the equation:
y=−5(x−6) y = -5(x - 6)

STEP 6

Distribute the slope −5 -5 on the right-hand side:
y=−5x+30 y = -5x + 30

STEP 7

The equation is already in slope-intercept form y=mx+b y = mx + b .
The equation of the line is:
y=−5x+30 y = -5x + 30

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