To find the equation of a line that goes through two points, you can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where "m" is the slope of the line and "b" is the y-intercept (the point where the line crosses the y-axis).
To find the slope of the line, you can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
In this case, we are given the points (4, 5) and (8, 7), so we can plug these values into the formula for the slope:
m = (7 - 5) / (8 - 4)
= 2 / 4
= 1/2
Now that we know the slope of the line, we can use the point-slope form of the equation of a line to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is any point on the line and "m" is the slope of the line.
In this case, we are given the point (4, 5), so we can plug these values into the formula:
y - 5 = (1/2)(x - 4)
y = (1/2)x + 3
So, the equation of the line that goes through (4,5) and (8,7) is y = (1/2)x + 3.
Therefore, the correct answer is (b) y = /2x+3.