Question

Write the equation of the line in point-slope form and in slope-intercept form.The line passes through the point (6,1) and has a slope of -1/2.

Answer 1

Explanation

The slope-intercept form of a line is given as;

$y=mx+b$

The point-slope form of a line is given as;

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

From the given question we have that;

$\begin{gathered} m=-\frac{1}{2} \\ (x_1,y_1)=(6,1) \end{gathered}$

Part A

Therefore, the point-slope equation can be expressed as;

Answer

$y-1=-\frac{1}{2}(x-6)$

Part B

To find the slope-intercept form of the line we will simplify the point-slope form. This can be seen below.

$\begin{gathered} y-1=-\frac{1}{2}(x-6) \\ y=-\frac{1}{2}x_{}+\frac{6}{2}+1 \\ y=-\frac{1}{2}x+3+1 \\ y=-\frac{1}{2}x+4 \end{gathered}$

Answer:

$y=-\frac{1}{2}x+4$