Question

right triangle abc is shown on the graph. if the point (-4, y) lies on the line that goes through side bc of the triangle, then what should be the value of y? the graph shows a coordinate plane with points a, b, c. b is at (0, 5), c is at (-3, 2), a is at (0, 2). the options are a. 0, b. -5, c. 1, d. -1

Explanation:

Step1: Find the slope of line BC

Points \( B(0, 5) \) and \( C(-3, 2) \). The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
So, \( m = \frac{2 - 5}{-3 - 0} = \frac{-3}{-3} = 1 \).

Step2: Use point - slope form to find the equation of line BC

Using point \( B(0, 5) \) and slope \( m = 1 \), the point - slope form is \( y - y_1 = m(x - x_1) \).
Substituting values: \( y - 5 = 1\times(x - 0) \), which simplifies to \( y = x + 5 \).

Step3: Find the value of \( y \) when \( x=-4 \)

Substitute \( x = - 4 \) into the equation \( y = x + 5 \).
\( y=-4 + 5=1 \).

Answer:

C