Question

The pair of points (6,y) and (10,-1) lie on a line with a slope 1(over)4. What is the value of y?

Answer 1

Use the formula to find the slope which is m= y2-y1 over x2-x2. The equation would look like 1/4= -1 -y over 10-6. First, you do the subtraction in the denominator and you get 4. The equation would look like 1/4=-1-y over 4.

Then, you multiply the 4 to both side in order to get rid of the fraction from the equation. You would then have 1=-1-y. You add -1 to both side and you would have 2=-y. Since the variable cannot be negative, you divide -1 from both side and get -2=y. Therefore the answer is y=-2.

Hope this helps.

Answer 2

The formula for Slope is m =
`(y_2 - y_1)/(x_2 - x_1)` where m is the slope and the x's and y's are your given coordinates. So, plug the given information into the formula and solve for y.

m =
`(y_2 - y_1)/(x_2 - x_1)` Plug in the given values

`(1)/(4)` =
`(-1 - y)/(10 - 6)` Cross multiply
10 - 6 = -4 - 4y Subtract
4 = -4 - 4y Add 4 to both sides
8 = -4y Divide both sides by -4
-2 = y Swich the sides to make it easier to read
y = -2

Check your answer by plugging -2 back into the equation with the other values.

[tex] \frac{1}{4} [/tex] =
`(-1 - (-2))/(10 - 6)` Simplify the double negative

`(1)/(4)` =
`(-1 + 2)/(10 - 6)` Simplify the numerator and denominator

`(1)/(4)` =
`(1)/(4)`

Since both sides equal each other, y = -2.