In the standard (x,y) coordinate plane, the graph of the linear equation y - 7 = -2(x + 3)… — ACT

In the standard $(x,y)$ coordinate plane, the graph of the linear equation $y - 7 = -2(x + 3)$ crosses the $y$ -axis. What is the $y$ -coordinate of this intersection point?

Answer: 1

Answer

The

y

-coordinate of the intersection point is

1

To find where the graph of the linear equation crosses the

y

-axis, substitute

x = 0

into the equation

y - 7 = -2(x + 3)

. This gives

y - 7 = -2(0 + 3)

, which simplifies to

y - 7 = -6

. Adding

7

to both sides results in

y = 1

. Thus, the

y

-coordinate of the intersection point is

1

Step-by-Step Solution

Substitute

x = 0

into the linear equation.

y - 7 = -2(0 + 3)

The graph of an equation crosses the

y

-axis (which defines the

y

-intercept) when the

x

-coordinate is equal to

0

Simplify the expression on the right side of the equation.

y - 7 = -6

Evaluating

-2(0 + 3)

yields

-2(3) = -6

Solve the simplified linear equation for

y

y = 1

Adding

7

to both sides isolates

y

, giving

y = -6 + 7 = 1

Key Concept

Finding the

y

-intercept of a line from its point-slope form equation

Question

Answer

Step-by-Step Solution

Key Concept

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