Can someone assist me in the right direction with this question?
Find an equation of the line containing the given pair of points. (-5,-6) (1,-3)
The equation needs to be in slope intercept form.
Thanks.
m=y2-y1/x2-x1
=(-3)-(-6)/1-(-5)
=3/6
=1/2
y=mx+b
y=1/2x+b
now use either of the points to solve for b
-3=1/2(1)+b
-3-1/2=b
2.5=b
so
y=0.5x+2.5
-3 - 1/2 = -7/2 not 2.5
so y = (1/2)x - 7/2
Of course! To find the equation of a line in slope-intercept form, we need two pieces of information: the slope of the line (m) and the y-intercept (b).
First, let's find the slope (m) using the given pair of points (-5,-6) and (1,-3). The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates into the formula:
m = (-3 - (-6)) / (1 - (-5))
m = (-3 + 6) / (1 + 5)
m = 3 / 6
m = 1/2
So, we've found that the slope is 1/2.
Next, we need to find the y-intercept (b). We can use the formula for the y-intercept:
b = y - mx
Let's choose one of the given points, (-5,-6), and substitute its coordinates along with the value of the slope into the formula:
b = -6 - (1/2)(-5)
b = -6 + 5/2
b = -12/2 + 5/2
b = -7/2
So, we found that the y-intercept is -7/2.
Now that we have the slope (m = 1/2) and the y-intercept (b = -7/2), we can write the equation of the line in slope-intercept form, which is:
y = mx + b
Plugging in the values we found, we get:
y = (1/2)x - 7/2
Therefore, the equation of the line containing the given pair of points (-5,-6) and (1,-3) in slope-intercept form is y = (1/2)x - 7/2.