Question

Find the value of x so that the line passing through the points will have the given slope: (x, 6) and (10, -3) with a slope of -3/2.
Answer

-13

4

13

-12

Answer 1

Well lets see...we use

\[\frac{ y_2 - y_1 }{ x_2 - x_1 }\] to find slope...we know the numerator of the slope = -3...so lets find out what we have

y2 - y1 = -3 - 6 = -9

how do we get from -9 to -3? we divide by 3....so this mean....to find the denominator...we need to find what number when subtracted from 10......and divided by 3....= 2

x2 - x1 = 10 - x

we know

\[\frac{ 10 - x }{ 3 } = 2\]

so multiply both sides by 3

\[10 - x = 6\]

subtract 10 from both sides

\[-x = -4\]

and multiply by -1

x = 4

so the 'x' must equal 4

Answer 2

Now lets check it

\[\frac{ y_2 - y_1 }{ x_2 - x_1 }\]

\[\frac{ -3 - 6 }{ 10 - 4 }\]

\[\frac{ -9 }{ 6 }\]

simplified down

\[-\frac{ 3 }{ 2 }\]

So it works out