Question

Find the equation of the line that has the given properties. Write the equation in slope-intercept form, if possible. 23) Contains (-2, -5); parallel to y=-1/2x-10

Answer 1

Answer:

y=-1/2x-6.

Explanation:

Comparing the given line with the slope-intercept form (y=mx+b):

$y=-\frac{1}{2}x-10\implies\text{Slope,m}=-\frac{1}{2}$

Two lines are parallel if they have the same slope.

Thus, the new line is required to have a slope of -1/2 and pass through the point (-2,-5).

Using the point-slope form:

$\begin{gathered} y-y_1=m(x-x_1)\text{ where:} \\ Slope,m=-\frac{1}{2} \\ Point,(x_1,y_1)=(-2,-5) \end{gathered}$

Substitute the points:

$\begin{gathered} y-(-5)=-\frac{1}{2}\lbrack x-(-2)\rbrack \\ y+5=-\frac{1}{2}(x+2)_{} \end{gathered}$

Finally, we express it in the slope-intercept form:

$\begin{gathered} y+5=-\frac{1}{2}x-1 \\ y=-\frac{1}{2}x-1-5 \\ \implies y=-\frac{1}{2}x-6 \end{gathered}$

The equation of the line that has the given properties is y=-1/2x-6.