Final answer:
To find the equation of the line, substitute the coordinates of the point into the equation and solve for the slope and y-intercept. The equation of the line is y = (5/4)x.
Step-by-step explanation:
To find the equation of the line given that m=a and it goes through the point (4,5), we need to determine the value of a. Since the line passes through the point (4,5), the coordinates (x,y) can be substituted into the equation. So, we have:
5 = a(4)
Solving for a, we divide both sides of the equation by 4:
a = 5/4
Now that we have the value of a, we can write the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept. Since m = a = 5/4, the equation becomes:
y = (5/4)x + b
To find the y-intercept, we can substitute the coordinates (4,5) into the equation:
5 = (5/4)(4) + b
Simplifying further:
5 = 5 + b
Subtracting 5 from both sides of the equation:
b = 0
Therefore, the equation of the line is:
y = (5/4)x + 0