Final answer:
To find the equation of the line in slope-intercept form, calculate the slope using the two points, then use one point to solve for the y-intercept. The resulting equation is y = -1/3x + 5/3.
Step-by-step explanation:
To write the equation of a line passing through the points ( –7, 4) and (5, 0) in slope-intercept form, you first need to calculate the slope of the line. The slope (m) is equal to the change in y divided by the change in x (m = Δy/Δx). Using the given points, you have:
m = (0 - 4) / (5 - ( –7)) = –4 / 12 = –1/3.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Now that we know the slope is –1/3, we need to find b. You can do this by substituting the slope and one of the given points into the equation to solve for b:
4 = ( –1/3)( –7) + b
b = 4 - (7/3)
b = (12/3) – (7/3)
b = 5/3
So the equation of our line in slope-intercept form is:
y = –1/3x + 5/3