Question

Find an Equation of the Line Given Two Points $(7,1)$and $(5,0)$. Write the equation in slope–intercept form.

Short answer

Equation of the line is:$y=\frac{1}{2}x-\frac{5}{2}$

Step-by-step solution

Given information

Here given two points are $(7,1)$and $(5,0)$.

Concept used

Here we have to use slope formula and slope - point formula to find an equation of a line.

slope =$m=\frac{y_2-y_1}{x_2-x_1}$

Slope - point formula: $y-y_1=m(x-x_1)$

Here we can use any one point from the given two points.

Explanation

Given two points are:$(7,1)$and $(5,0)$.

Using slope formula,

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

role="math" localid="1644302591019" $\Rightarrow m=\frac{0-1}{5-7}$

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

Using Slope - point formula,

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

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

Conclusion

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