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Math  /  Algebra

QuestionProblem\#1. Find the yy-intercept ( 0 , \qquad ) for a line with a slope of m=−2m=-2 that goes through (−1,3)(-1,3). Write the equation for the line. y=y= \qquad Use spaghetti or a ruler to help you figure out the yy-intercept. Draw the line.

Studdy Solution

STEP 1

1. We are given a line with a slope of m=−2 m = -2 .
2. The line passes through the point (−1,3)(-1, 3).
3. We need to find the y y -intercept of the line.
4. We need to write the equation of the line in slope-intercept form, y=mx+b y = mx + b .

STEP 2

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

STEP 3

Use the point-slope form of a line, which 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=−2 m = -2 and (−1,3)(-1, 3) into the equation:
y−3=−2(x+1) y - 3 = -2(x + 1)

STEP 4

Convert the equation to slope-intercept form y=mx+b y = mx + b .
First, distribute the slope on the right side:
y−3=−2x−2 y - 3 = -2x - 2
Add 3 to both sides to solve for y y :
y=−2x−2+3 y = -2x - 2 + 3
Simplify the equation:
y=−2x+1 y = -2x + 1

STEP 5

Identify the y y -intercept from the equation y=−2x+1 y = -2x + 1 .
The y y -intercept is the constant term when x=0 x = 0 , which is:
b=1 b = 1

STEP 6

Write the equation of the line using the slope-intercept form:
y=−2x+1 y = -2x + 1
The y y -intercept is (0,1) (0, 1) .

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