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

The formula for Slope is m = $\frac{y_2 - y_1}{x_2 - x_1}$ 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 = $\frac{y_2 - y_1}{x_2 - x_1}$   Plug in the given values
$\frac{1}{4}$ = $\frac{-1 - y}{10 - 6}$   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] = $\frac{-1 - (-2)}{10 - 6}$   Simplify the double negative
$\frac{1}{4}$ = $\frac{-1 + 2}{10 - 6}$   Simplify the numerator and denominator
$\frac{1}{4}$ = $\frac{1}{4}$

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

Answer 2

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.