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Math  /  Algebra

QuestionQuestion Watch Video Show Examples What is the equation of the line that passes through the point (6,0)(6,0) and has a slope of −56-\frac{5}{6} ?
Answer Attempt 2 out of 3

Studdy Solution

STEP 1

1. We need to find the equation of a line.
2. The line passes through the point (6,0)(6, 0).
3. The line has a slope of −56-\frac{5}{6}.

STEP 2

1. Use the point-slope form of a line equation.
2. Substitute the given point and slope into the point-slope form.
3. Simplify the equation to the slope-intercept form.

STEP 3

Use the point-slope form of a line equation, which is:
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 point (6,0)(6, 0) and slope −56-\frac{5}{6} into the point-slope form:
y−0=−56(x−6) y - 0 = -\frac{5}{6}(x - 6)

STEP 5

Simplify the equation to the slope-intercept form y=mx+b y = mx + b .
Distribute the slope on the right side:
y=−56x+56×6 y = -\frac{5}{6}x + \frac{5}{6} \times 6
Calculate the constant term:
y=−56x+5 y = -\frac{5}{6}x + 5
The equation of the line is:
y=−56x+5 y = -\frac{5}{6}x + 5

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