Question

In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.

(7, 1) and (5, 0)

Short answer

Equation of the line passing through the point (7, 1) and (5, 0) is: $y=\frac{1}{2}x-\frac{5}{2}$.

Step-by-step solution

Step 1. Given information

We have given two points (7, 1) and (5, 0).

Step 2. Concepts

Here we can use slope and slope - point formula to find the equation of the line.

Slope = $\frac{y_2-y_1}{x_2-x_1}$

Slope - point formula:

$y-y_1=m(x-x_1)$

Step 3. Explanation

Using slope formula,

$m=\frac{0-1}{5-7}$

$\Rightarrow m=\frac{1}{2}$

Using slope - point formula,

$y-y_1=m(x-x_1)$

Substituting slope and one of the given point,

$y-0=\frac{1}{2}(x-5)$

Simplifying it,

$y=\frac{1}{2}x-\frac{5}{2}$

Step 4. Conclusion

Hence, equation of the line passing through the points (7, 1) and (5, 0) is,$y=\frac{1}{2}x-\frac{5}{2}$