Final answer:
The equation of the line that passes through the points (-4,0) and (6,5) is determined by first calculating the slope, which is 0.5, and then using the point-slope form to derive the equation y = 0.5x + 2.
Step-by-step explanation:
To write the equation of the line that passes through the points (-4,0) and (6,5), we need to find the slope (m) of the line. The slope can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula gives us:
m = (5 - 0) / (6 - (-4)) = 5 / 10 = 0.5
Now that we have the slope, we can use the point-slope form of a line, y - y1 = m(x - x1), substituting either point and the slope. Using point (-4,0), the equation is:
y - 0 = 0.5(x - (-4))
y = 0.5x + 2
The equation of the line that passes through the points (-4,0) and (6,5) is y = 0.5x + 2.