Final answer:
To find the distance between the line y = -7/4 + 2/4 and the point (-2,4), we use the formula: distance = | Ax + By + C | / √(A^2 + B^2). Plugging in the values, the distance is 30/√65 or approximately 3.71.
Step-by-step explanation:
To find the distance between a point and a line, you can use the formula:
distance = | Ax + By + C | / √(A^2 + B^2)
In this case, the equation of the line is y = -7/4x + 2/4 and the point is (-2,4).
First, we need to find A, B, and C. Since the equation of the line is in slope-intercept form (y = mx + b), A = -7/4, B = 1, and C = 2/4.
Plugging these values into the formula, we get:
distance = | (-7/4)(-2) + (1)(4) + (2/4) | / √((-7/4)^2 + (1)^2)
= | 7/2 + 4/4 + 2/4 | / √((49/16) + 1)
= | 15/4 | / √(65/16)
= 15/4 √(16/65)
= 15/4 √(4/65)
= 15/4 * 2/√65
= 30/√65.
Therefore, the distance between the line y = -7/4x + 2/4 and the point (-2,4) is 30/√65 or approximately 3.71.