What is the equation of the line that passes through the points (−3,4) and (−6,3)? Write the answer in slope-intercept form.
The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the points (-3, 4) and (-6, 3):
m = (3 - 4) / (-6 - (-3))
= -1 / (-6 + 3)
= -1 / -3
= 1/3.
Now that we have the slope, we can substitute one of the given points into the equation y = mx + b to find the y-intercept. Using (-3, 4):
4 = (1/3)(-3) + b
4 = -1 + b
4 + 1 = b
b = 5.
Therefore, the equation of the line in slope-intercept form is:
y = (1/3)x + 5.