Write an equation in slope-intercept form for the line that passes through the two points.
(2, 7) and (-4, 4)
Slope-intercept form of a linear equation is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, let's find the slope (m) of the line that passes through the points (2,7) and (-4,4).
The formula for finding the slope between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Let's assign the values from our points:
x1 = 2, y1 = 7
x2 = -4, y2 = 4
Now plug the values into the slope formula:
m = (4 - 7) / (-4 - 2)
m = (-3) / (-6)
m = 1/2
So the slope of the line is 1/2.
Now, we need to find the y-intercept (b). We can do this by using one of our points and the slope in the slope-intercept equation. Let's use point (2,7):
7 = (1/2)*2 + b
Now solve for b:
7 = 1 + b
b = 7 - 1
b = 6
Now that we have both m and b, we can write the equation of the line:
y = (1/2)x + 6
Therefore, the equation of the line in slope-intercept form passing through the points (2, 7) and (-4, 4) is y = 1/2x + 6.