Question

alternative activity
equation | y-intercepts | choices
$2x + 3y = -12$ | | $(0, -6)$
$-x - y = 1$ | | $(0, 4)$
$-8x - 10y = -40$ | | $(0, -4)$
$-6x - 5y = 30$ | | $(0, -1)$
alternative activity
example

Explanation:

To find the y - intercept of a linear equation in the form \(Ax + By = C\), we set \(x = 0\) and solve for \(y\).

Step 1: Find the y - intercept of \(2x+3y=-12\)

Set \(x = 0\) in the equation \(2x + 3y=-12\). Then the equation becomes \(2(0)+3y=-12\), which simplifies to \(3y=-12\). Divide both sides by 3: \(y=\frac{-12}{3}=-4\). So the y - intercept is \((0, - 4)\).

Step 2: Find the y - intercept of \(-x - y=1\)

Set \(x = 0\) in the equation \(-x - y = 1\). Then the equation becomes \(-0 - y=1\), which simplifies to \(-y = 1\). Multiply both sides by - 1: \(y=-1\). So the y - intercept is \((0, - 1)\).

Step 3: Find the y - intercept of \(-8x-10y=-40\)

Set \(x = 0\) in the equation \(-8x-10y=-40\). Then the equation becomes \(-8(0)-10y=-40\), which simplifies to \(-10y=-40\). Divide both sides by - 10: \(y=\frac{-40}{-10} = 4\). So the y - intercept is \((0,4)\).

Step 4: Find the y - intercept of \(-6x-5y=30\)

Set \(x = 0\) in the equation \(-6x-5y=30\). Then the equation becomes \(-6(0)-5y=30\), which simplifies to \(-5y=30\). Divide both sides by - 5: \(y=\frac{30}{-5}=-6\). So the y - intercept is \((0, - 6)\).

Answer:

For \(2x + 3y=-12\), y - intercept is \((0, - 4)\)

For \(-x - y = 1\), y - intercept is \((0, - 1)\)

For \(-8x-10y=-40\), y - intercept is \((0,4)\)

For \(-6x - 5y=30\), y - intercept is \((0, - 6)\)