Studdy AI Logo
Math  /  Algebra

Questionview Question 22, *5.6.7 HW Score: 80\%, 24 of 30 points Save
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (−2,−6);y=−2x+4(-2,-6) ; y=-2 x+4
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 need to find the equation of a line in slope-intercept form.
2. The line must pass through the point (−2,−6)(-2, -6).
3. The line is parallel to the given line with the equation y=−2x+4y = -2x + 4.
4. Parallel lines have the same slope.

STEP 2

1. Identify the slope of the given line.
2. Use the slope-point form to find the equation of the new line.
3. Convert the equation to slope-intercept form.

STEP 3

Identify the slope of the given line.
The given line is y=−2x+4y = -2x + 4, which is already in slope-intercept form y=mx+by = mx + b, where mm is the slope.
Thus, the slope mm is −2-2.

STEP 4

Use the slope-point form to find the equation of the new line.
The slope-point form of a line is given by:
y−y1=m(x−x1) y - y_1 = m(x - x_1)
where mm is the slope and (x1,y1)(x_1, y_1) is the point the line passes through.
Substitute m=−2m = -2, x1=−2x_1 = -2, and y1=−6y_1 = -6:
y−(−6)=−2(x−(−2)) y - (-6) = -2(x - (-2))
Simplify the equation:
y+6=−2(x+2) y + 6 = -2(x + 2)

STEP 5

Convert the equation to slope-intercept form.
Distribute the −2-2 on the right side:
y+6=−2x−4 y + 6 = -2x - 4
Subtract 6 from both sides to solve for yy:
y=−2x−4−6 y = -2x - 4 - 6
y=−2x−10 y = -2x - 10
The equation of the line in slope-intercept form is:
y=−2x−10 y = -2x - 10

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord