Write the slope-intercept equation for the line through (3, 7) and (9, 3)
The slope-intercept form is y = mx + b
7 = m*3 + b
3 = m*9 + b
Subtract second equation from the first, to eliminate the unknown b.
4 = -6m
m = -2/3
7 = -2 + b
b = 9
y = -(2/3)x + 9
To write the slope-intercept equation for a line, we need to find the slope and the y-intercept.
The formula for the slope is given by:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
We can plug in the given points, (3, 7) and (9, 3), into the formula to find the slope:
m = (3 - 7) / (9 - 3)
= -4 / 6
= -2/3
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
We can choose either of the given points to use as (x1, y1). Let's use the point (3, 7):
y - 7 = (-2/3)(x - 3)
Now, we can simplify this equation to the slope-intercept form, which is in the form y = mx + b:
y - 7 = (-2/3)x + 2
y = (-2/3)x + 2 + 7
y = (-2/3)x + 9
Therefore, the slope-intercept equation for the line through (3, 7) and (9, 3) is y = (-2/3)x + 9.