Q. Find the y-intercept of the line represented by the equation: \[ -12 = -2x – 4y \]

Q: How do I find the y-intercept?

Set x=0 and solve: -12=-2(0)-4y, so -12=-4y and y=3. The y-intercept is (0,3)..

Q: How do I write the equation in slope-intercept form?

Solve for y: -12=-2x-4y gives 2x-12=-4y, so y=-\tfrac{1}{2}x+3.

Q: What is the slope of the line?

From y=-\tfrac{1}{2}x+3 the slope is m=-\tfrac{1}{2}.

Q: How do I find the x-intercept?

Set y=0: -12=-2x-4(0) so -12=-2x and x=6. X-intercept is (6,0).

Q: How can I quickly sketch the line?

Plot the y-intercept (0,3) ; use slope -\tfrac{1}{2} : from (0,3) go right 2, down 1 to get another point, then draw the line through them.

Q: Is the y-intercept positive or negative?

Is the y-intercept positive or negative?

Q: How can I check whether a point lies on this line?

Substitute the point x,y into -12=-2x-4y. If equality holds, the point is on the line (e.g., (0,3) gives -12=-12).

Q: How do I write the equation in standard form with integer coefficients?

Start with -2x-4y=-12 . Multiply by -1 to get 2x+4y=12 , then simplify to x+2y=6 .

Answer

Set x=0: \( -12 = -2(0) – 4y \) which gives \( -12 = -4y \) and hence \( y = 3 \). Final answer: y-intercept \( (0,3) \).

Detailed Explanation

We are asked for the y-intercept of the line given by the equation \( -12 = -2x – 4y \). The y-intercept is the value of y when \( x = 0 \).
Substitute \( x = 0 \) into the equation: \( -12 = -2(0) – 4y \).
Simplify the right-hand side: \( -12 = 0 – 4y \), so \( -12 = -4y \).
Solve for y by dividing both sides by \(-4\): \( y = \dfrac{-12}{-4} = 3 \).
The y-intercept is the point where \( x = 0 \) and \( y = 3 \), so the y-intercept is (0, 3). The y-coordinate (the intercept value) is 3.

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Algebra FAQs

How do I find the \(y\)-intercept?

Set \(x=0\) and solve: \(-12=-2(0)-4y\), so \(-12=-4y\) and \(y=3\). The y-intercept is \((0,3)\)..

How do I write the equation in slope-intercept form?

Solve for \(y\): \(-12=-2x-4y\) gives \(2x-12=-4y\), so \(y=-\tfrac{1}{2}x+3\).

What is the slope of the line?

From \(y=-\tfrac{1}{2}x+3\) the slope is \(m=-\tfrac{1}{2}\).

How do I find the \(x\)-intercept?

Set \(y=0\): \(-12=-2x-4(0)\) so \(-12=-2x\) and \(x=6\). X-intercept is \((6,0)\).

How can I quickly sketch the line?

Plot the y-intercept \( (0,3) \); use slope \( -\tfrac{1}{2} \): from \( (0,3) \) go right 2, down 1 to get another point, then draw the line through them.

Is the \(y\)-intercept positive or negative?

How can I check whether a point lies on this line?

Substitute the point \(x,y\) into \(-12=-2x-4y\). If equality holds, the point is on the line (e.g., \((0,3)\) gives \(-12=-12\)).

How do I write the equation in standard form with integer coefficients?

Start with \( -2x-4y=-12 \). Multiply by \( -1 \) to get \( 2x+4y=12 \), then simplify to \( x+2y=6 \).

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