Question

Use an equation to find the value of k so that the line that passes through the given points has the given slope. (

4,−4), (k,−1); slope=34

Answer 1

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (4, -4) and (k, -1) and the slope m = 34.

Substitute:

$\dfrac{-1-(-4)}{k-4}=34\\\\\dfrac{3}{k-4}=\dfrac{34}{1}\qquad|\text{cross multiply}\\\\34(k-4)=3\qquad|\text{use distributive property}\\\\34k-136=3\qquad|+136\\\\34k=139\qquad|:34\\\\k=\dfrac{139}{34}$

Answer 2

Using the equation of slope of a straight line, the value of k is 4.09.

Given the following points:

• Points on the x-axis = (4, k)

• Points on the y-axis = (-4, -1)

• Slope = 34.

To find the value of k, we would use the equation of slope of a straight line:

$Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the points and slope into the formula, we have;

$34 = \frac{-1\; - \;[-4]}{k \;-\;4}\\\\34 = \frac{-1\; + \;4}{k \;-\;4}\\\\34 = \frac{3}{k \;-\;4}$

Cross-multiplying, we have:

$34(k\; - \;4) = 3\\\\34k - 136 = 3\\\\34k = 136 + 3\\\\34k = 139\\\\k = \frac{139}{34}$

k = 4.09

Therefore, the value of k is 4.09.

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