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)=-(1)/(2)(x-(-3)) \\ \\ y+4=-(1)/(2)(x+3) \end{gathered}`

Therefore, the equation in point slope form is:

`y+4=-(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=-(1)/(2)(-3)+b \\ \\ -4=(3)/(2)+b \\ \\ \end{gathered}`

Subtract 3/2 from both sides:

`\begin{gathered} -4-(3)/(2)=(3)/(2)-(3)/(2)+b \\ \\ -(4)/(1)-(3)/(2)=b \\ \\ (-8-3)/(2)=b \\ \\ -(11)/(2)=b \\ \\ b=-(11)/(2) \end{gathered}`

Therefore, the slope intercept form of the line is:

`y=-(1)/(2)x-(11)/(2)`

ANSWER:

Point-slope form:

`y+4=-(1)/(2)(x+3)`

Slope intercept form:

`y=-(1)/(2)x-(11)/(2)`