right triangle ABC is shown on the graph below. If the point (-4,y) lies in the line that goes through side BC of the triangle, then what should be Y?
the graph shows a triangle with three points A:0,2 B:0,5 C:-3,2
To find the value of y, we need to determine the equation of the line that passes through the points B and C.
First, we find the slope of the line using the coordinates of points B and C:
m = (y2 - y1) / (x2 - x1)
m = (2 - 5) / (-3 - 0)
m = -3 / -3
m = 1
The slope of the line passing through points B and C is 1.
Next, we use the point-slope form of a linear equation, which is given by:
y - y1 = m(x - x1)
Using the point B (0, 5) or C (-3, 2), we can write the equation of the line as:
y - 5 = 1(x - 0)
y - 5 = x
Finally, substituting x = -4 into the equation, we can solve for y:
y - 5 = -4
y = 1
Therefore, y = 1.