Question

Find the equation of the line in slope-intercept form containing the points (6, -1) and (-3, 2).

Answer 1

To find the equation of the line in slope-intercept form containing the points (6, -1) and (-3, 2), we first find the slope using the formula m = (y2 - y1) / (x2 - x1). We then substitute the slope and one of the points into the equation y = mx + b to solve for the y-intercept (b). Finally, we write the equation of the line in slope-intercept form.

Step-by-step explanation:

To find the equation of the line in slope-intercept form containing the points (6, -1) and (-3, 2), we can use the slope-intercept form equation: y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope. The slope (m) is given by the formula: m = (y2 - y1) / (x2 - x1). Substituting the given coordinates, we get m = (2 - (-1)) / (-3 - 6) = 3 / -9 = -1/3.

Next, we can choose one of the points and substitute the coordinates into the equation y = mx + b to solve for b. Using the point (6, -1), we have -1 = (-1/3)(6) + b. Solving for b, we get b = -1 + 2 = 1.

Therefore, the equation of the line in slope-intercept form is y = -1/3x + 1.

Answer 2

slope intercepf is y=mx+b wherem=slope and b= y intercept
slope is found by doing
(y1-y2)/(x1-x2)
points are (6,-1) and (-3,2)
(x,y)
x1=6
y1=-1
x2=-3
y2=2
subsitute
(-1-2)/(6-(-2))=-3/(6+2)=-3/8
slope=-3/8
subsitute
y=-3/8x+b
subsitute and solve for b
(-3,2)
x=-3
y=2
2=-3/8(-3)+b
2=9/8+b
2=16/8
subtract 9/8 from both sides
16/8-9/8=b
7/8=b
y=-3/9x+7/8 is the equation