Final answer:
The equation of a line with a slope of 4/5 that passes through the point (4,3) is not one of the provided options. By using the point-slope form, we can derive the correct equation as y = (4/5)x - 1/5.
Step-by-step explanation:
To find the equation of a line with a given slope that passes through a specified point, you can use the point-slope form of a line's equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Since we have the slope m = 4/5 and the point (4, 3), we can plug these values into the point-slope form:
y - 3 = (4/5)(x - 4)
To find the equation in slope-intercept form (y = mx + b), we solve for y:
Distribute the slope 4/5 to both terms inside the parentheses:
y - 3 = (4/5)x - (4/5)×4
y - 3 = (4/5)x - 16/5
Now, add 3 to both sides to isolate y:
y = (4/5)x - 16/5 + 15/5
y = (4/5)x - 1/5
Thus, none of the given options a), b), c) or d) is correct. The equation for the line is y = (4/5)x - 1/5.