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Math  /  Algebra

QuestionUse the given conditions to write an equation for the line in point-slope form and in slope-intercept form.  Slope =−14, passing through (9,−1)\text { Slope }=-\frac{1}{4}, \text { passing through }(9,-1)
Write an equation for the line in point-slope form. □\square (Simplify your answer. Use integers or fractions for any numbers in the equation.) Write an equation for the line in slope-intercept form. □\square (Simplify your answer. Use integers or fractions for any numbers in the equation.)

Studdy Solution

STEP 1

1. We are given the slope of the line, m=−14 m = -\frac{1}{4} .
2. The line passes through the point (9,−1) (9, -1) .
3. We need to write the equation of the line in both point-slope form and slope-intercept form.

STEP 2

1. Write the equation in point-slope form.
2. Convert the equation to slope-intercept form.

STEP 3

Write the equation in point-slope form.
The point-slope form of a line 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.
Substitute m=−14 m = -\frac{1}{4} , x1=9 x_1 = 9 , and y1=−1 y_1 = -1 into the equation:
y−(−1)=−14(x−9) y - (-1) = -\frac{1}{4}(x - 9)
Simplify the equation:
y+1=−14(x−9) y + 1 = -\frac{1}{4}(x - 9)

STEP 4

Convert the equation to slope-intercept form.
The slope-intercept form of a line is given by:
y=mx+b y = mx + b
Start with the point-slope form equation:
y+1=−14(x−9) y + 1 = -\frac{1}{4}(x - 9)
Distribute the slope on the right side:
y+1=−14x+94 y + 1 = -\frac{1}{4}x + \frac{9}{4}
Subtract 1 from both sides to solve for y y :
y=−14x+94−1 y = -\frac{1}{4}x + \frac{9}{4} - 1
Convert 1 to a fraction with a denominator of 4:
y=−14x+94−44 y = -\frac{1}{4}x + \frac{9}{4} - \frac{4}{4}
Combine the fractions:
y=−14x+54 y = -\frac{1}{4}x + \frac{5}{4}
The equation in point-slope form is:
y+1=−14(x−9) y + 1 = -\frac{1}{4}(x - 9)
The equation in slope-intercept form is:
y=−14x+54 y = -\frac{1}{4}x + \frac{5}{4}

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