Question

1. write the equation of the line that goes through the point (-2,8) and is perpendicular to the line $y + 3 = -\frac{2}{7}(x - 4)$. determine each form.

point - slope form \t slope - intercept form

1. write the equation of the line that is parallel to $x = 12$ and passes through $(-23,7)$.
2. write the equation of the line in standard form that passes through $(-4,10)$ and is parallel to the line shown on the coordinate grid.

(coordinate grid with x from -10 to 5 and y from -5 to 10, a line passing through the origin with positive slope)
standard form of parallel line

Explanation:

Problem 2:

Step1: Identify line type

The line \( x = 12 \) is a vertical line (undefined slope). Parallel lines to vertical lines are also vertical.

Step2: Determine equation

A vertical line passing through \( (-23, 7) \) has the equation \( x = -23 \), since all points on this line have \( x \)-coordinate \( -23 \).

Step1: Find slope of given line

The given line passes through the origin \((0,0)\) and, from the graph, another point like \((1, 2)\) (estimating from the grid). Slope \( m = \frac{2 - 0}{1 - 0} = 2 \).

Step2: Use point - slope form

The line we want is parallel, so slope \( m = 2 \). Using point \((-4, 10)\), point - slope form is \( y - 10 = 2(x + 4) \).

Step3: Convert to standard form

Expand: \( y - 10 = 2x + 8 \). Rearrange to \( 2x - y = -18 \) (standard form \( Ax + By = C \), \( A\geq0 \)).

Answer:

\( x = -23 \)

Problem 3: