Answer:
y = -(7x/5) - (9/5)
Explanation:
Line f has an equation of y + 4 = (5/7)(x + 3). We want to find the equation of line g, which is perpendicular to line f and passes through the point (-2, 1).
To find the equation of line g, we need to determine its slope. The slope of line f is (5/7) because the equation is in the form y = mx + b, where m represents the slope.
Since line g is perpendicular to line f, its slope will be the negative reciprocal of the slope of line f. To find the negative reciprocal, we flip the fraction and change the sign. So, the slope of line g is -(7/5).
We know that line g passes through the point (-2, 1). We can use this information to find the equation of line g using the point-slope form of a linear equation: y - y1 = m(x - x1).
Substituting the values, we have: y - 1 = -(7/5)(x - (-2)).
Simplifying, we get: y - 1 = -(7/5)(x + 2).
Distributing -(7/5) to (x + 2), we have: y - 1 = -(7/5)x - (14/5).
To isolate y, add 1 to both sides: y = -(7/5)x - (14/5) + 1.
Simplifying, we get: y = -(7/5)x - (14/5) + 5/5.
Combining fractions, we have: y = -(7/5)x - (9/5).
Therefore, the equation of line g in a student-friendly format is y = -(7/5)x - (9/5).