Write an equation in slope-intercept form for the line that passes through the two points.
(2, 7) and (-4, 4)
To write the equation of a line in slope-intercept form (y = mx + b), you need to determine the slope (m) and the y-intercept (b).
First, calculate the slope using the two given points (x1, y1) = (2, 7) and (x2, y2) = (-4, 4):
Slope (m) = (y2 - y1) / (x2 - x1)
m = (4 - 7) / (-4 - 2)
m = (-3) / (-6)
m = 1/2
Now that we have the slope, we can use one of the points to solve for the y-intercept (b). We'll use the point (2, 7). Substitute the x and y values from the point into the slope-intercept equation along with the slope:
7 = (1/2)*2 + b
Now solve for b:
7 = 1 + b
7 - 1 = b
b = 6
So, the equation of the line in slope-intercept form is:
y = (1/2)x + 6