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Math  /  Algebra

Questionthrough the point (−5,18)(-5,18). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. □\square

Studdy Solution

STEP 1

1. We are given a slope of 25 \frac{2}{5} .
2. The line passes through the point (−5,18)(-5, 18).
3. We need to write the equation of the line in slope-intercept form y=mx+b y = mx + b .

STEP 2

1. Identify the slope and the point.
2. Use the point-slope form of a line.
3. Convert to slope-intercept form.
4. Simplify the equation.

STEP 3

Identify the slope and the point. The slope m m is given as 25 \frac{2}{5} and the point is (−5,18)(-5, 18).

STEP 4

Use the point-slope form of a line, which is y−y1=m(x−x1) y - y_1 = m(x - x_1) , where (x1,y1) (x_1, y_1) is the point (−5,18)(-5, 18).
Substitute the given values into the point-slope form:
y−18=25(x+5) y - 18 = \frac{2}{5}(x + 5)

STEP 5

Convert to slope-intercept form by solving for y y .
First, distribute the slope on the right side:
y−18=25x+25×5 y - 18 = \frac{2}{5}x + \frac{2}{5} \times 5
y−18=25x+2 y - 18 = \frac{2}{5}x + 2
Add 18 to both sides to solve for y y :
y=25x+2+18 y = \frac{2}{5}x + 2 + 18
y=25x+20 y = \frac{2}{5}x + 20

STEP 6

The equation is already in slope-intercept form and simplified.
The equation of the line is:
y=25x+20 y = \frac{2}{5}x + 20

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