Question

write the equation in point slope and slope intercept form of a line that passes through the given point (-3, -4), and has the given slope m = -1/2

Answer 1

Question 1.

Given the point:

(-3, -4)

Slope, m = - 1/2

Let's write the equation of the line that passes through the given point with the slope in point-slope form and slope intercept form.

• Point slope form:

Apply the point-slope equation:

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

Now substitute -1/2 for m, then input (-3, -4) for x1 and y1 in the equation above.

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

Therefore, the equation in point slope form is:

$y+4=-\frac{1}{2}(x+3)$

• SLope intercept form:

Apply the slope intercept form of a linear equation:

$y=mx+b$

Where m is the slope and b is the y-intercept.

Substitute the following:

-1/2 for m

(-3, -4) for (x, y)

Then solve for b.

$\begin{gathered} -4=-\frac{1}{2}(-3)+b \\ \\ -4=\frac{3}{2}+b \\ \\ \end{gathered}$

Subtract 3/2 from both sides:

$\begin{gathered} -4-\frac{3}{2}=\frac{3}{2}-\frac{3}{2}+b \\ \\ -\frac{4}{1}-\frac{3}{2}=b \\ \\ \frac{-8-3}{2}=b \\ \\ -\frac{11}{2}=b \\ \\ b=-\frac{11}{2} \end{gathered}$

Therefore, the slope intercept form of the line is:

$y=-\frac{1}{2}x-\frac{11}{2}$

ANSWER:

Point-slope form:

$y+4=-\frac{1}{2}(x+3)$

Slope intercept form:

$y=-\frac{1}{2}x-\frac{11}{2}$