Write the equation passing through the points (-9, 6 ) and (1, -5). The worksheet has multiple choice, so I know y intercept is either 39/10 or -39/10.
I have -11/10x plus b
then -11 (1) is -11
10(1) is 10
Then -5 plus 11/10
I change -5 to -15/10 but I'm getting -26/10.
What am I doing wrong?
Given P1(-9, 6) and P2(1, -5)
If the line is not vertical, the line through the two points has a slope of
m=(y2-y1)/(x2-x1)
=(-5-6)/(1-(-9)
=-11/10
This should eliminate some of the choices.
To find the intercept, you can use
(y-y1)=m(x-x1)
y=-(11/10)(x-(-9)+6
=-(11/10)x - 39/10
confirming one of your two options.
In order to find the equation passing through the given points (-9, 6) and (1, -5), we need to determine both the slope and the y-intercept of the equation.
To calculate the slope (m), we use the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-9, 6) and (1, -5), we substitute the values into the slope formula:
m = (-5 - 6) / (1 - (-9))
= (-5 - 6) / (1 + 9)
= -11 / 10
Now that we have the slope (m), we can use it along with one of the points to find the equation in point-slope form:
y - y1 = m(x - x1)
Picking the point (-9, 6):
y - 6 = (-11/10)(x - (-9))
y - 6 = (-11/10)(x + 9)
Expanding the equation:
y - 6 = (-11/10)x - 99/10
To convert the equation to slope-intercept form (y = mx + b), isolate the y-term:
y = (-11/10)x - 99/10 + 6
y = (-11/10)x - 99/10 + 60/10
Combining like terms:
y = (-11/10)x - 39/10
Therefore, the equation passing through the points (-9, 6) and (1, -5) is y = (-11/10)x - 39/10.
Regarding your calculation, when you used -5 as -15/10, you correctly converted it to an equivalent fraction. However, when adding 11/10, it seems you made an error. To add fractions, the denominators must be the same:
-15/10 + 11/10 = (-15 + 11) / 10
= -4/10
= -2/5
Therefore, the correct value to use in the equation for the change of y is -2/5, not -26/10.