Write an equation for a line passing through the points (-1,8 and (0,5)

Well, let's see. To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation, which is y = mx + b.

First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) = (-1, 8) and (x2, y2) = (0, 5).

m = (5 - 8) / (0 - (-1))
= -3 / 1
= -3

Now, we have the slope (m = -3).

Next, we can plug one of the given points into the equation to find the y-intercept (b). Let's use (0, 5):

5 = (-3)(0) + b
5 = b

So, the y-intercept (b) is 5.

Finally, we can put it all together to form the equation:

y = -3x + 5

Voilà! That's our equation for a line passing through the points (-1,8) and (0,5).

To find the equation of the line passing through the points (-1,8) and (0,5), we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of a point on the line, and m is the slope of the line.

First, let's find the slope (m) using the coordinates of the two given points:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates (-1,8) and (0,5) into the slope formula, we get:

m = (5 - 8) / (0 - (-1))
= -3 / 1
= -3

Now that we have the slope, we can choose either of the two given points to substitute into the point-slope form. Let's use the point (-1,8):

y - 8 = -3(x - (-1))
y - 8 = -3(x + 1)
y - 8 = -3x - 3
y = -3x + 5

Therefore, the equation of the line passing through the points (-1,8) and (0,5) is y = -3x + 5.

To write an equation for a line passing through two points, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

where "m" is the slope of the line, and "b" is the y-intercept (the point where the line intersects the y-axis).

First, let's find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Let's substitute the coordinates of the two given points into the formula:

m = (5 - 8) / (0 - (-1))
= -3 / (0 + 1)
= -3 / 1
= -3

Now that we have the slope (m = -3), we can substitute it into the slope-intercept form equation along with the coordinates of one of the given points to find the y-intercept (b). Let's use the point (-1, 8):

y = mx + b
8 = (-3)(-1) + b
8 = 3 + b

Now, solve for b:

b = 8 - 3
b = 5

So, the y-intercept (b) is 5.

Now, substituting the slope (m = -3) and the y-intercept (b = 5) into the slope-intercept form equation, we have the equation for the line:

y = -3x + 5

Therefore, the equation for the line passing through the points (-1,8) and (0,5) is y = -3x + 5.

The two-point form of a straight line:

y - y1 = ( y2 - y1 ) ( x - x1 ) / ( x2 - x1 )

In this case:

x1 = 1 , y1 = - 8

x2 = 0 , y2 = 5

y - y1 = ( y2 - y1 ) ( x - x1 ) / ( x2 - x1 )

y - ( - 8 ) = [ 5 - ( - 8 ) ] ∙ ( x - 1 ) / ( 0 - 1 )

y + 8 = ( 5 + 8 ) ∙ ( x - 1 ) / - 1

y + 8 = 13 ∙ ( x - 1 ) / - 1

y + 8 = - 13 ∙ ( x - 1 )

y + 8 = - 13 ∙ x - 13 ∙ ( -1 )

y + 8 = - 13 x + 13

Subtract 8 to both sides

y = - 13 x + 5