Answer:
y = (4/5)x + 17/5
Explanation:
To find the equation of the line with a given slope (m) and passing through a given point (x1, y1), you can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
In your case, the given slope is m = 4/5, and the given point is (x1, y1) = (2, 5).
Now, plug these values into the point-slope equation:
y - 5 = (4/5)(x - 2)
To get the equation in a more standard form, you can multiply through by 5 to eliminate the fraction:
5(y - 5) = 4(x - 2)
Expand and simplify:
5y - 25 = 4x - 8
Now, rearrange the equation to isolate y:
5y = 4x - 8 + 25
5y = 4x + 17
Finally, divide both sides by 5 to solve for y and get the equation in slope-intercept form (y = mx + b):
y = (4/5)x + 17/5
So, the equation of the line with a slope of 4/5 and passing through the point (2, 5) is:
y = (4/5)x + 17/5