Question

6. A line goes through these two points, (-4,-1) an (-9,-5).A. Find an equation for this line in point slope form.B. Find the equation for this line in slope intercept form. Be sure to show your work.C. If the y-coordinate of a point on this line is 7, what is the x-coordinate of this point?7. Consider the line below.A. Find two points on this linn

Answer 1

A, B) y=4/5x +11/5

C) x=6

6) Since we have those two points, we can find out the slope between them using the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{-5-(-1)}{-9-(-4)}=\frac{-4}{-5}=\frac{4}{5}$

A) In the point-slope form, we can write out the following formula and then plug into that the coordinates the slope found above considering point (-4,-1):

$\begin{gathered} (y-y_1)=m(x-x_1) \\ y-(-1)=\frac{4}{5}(x+4) \\ y+1=\frac{4}{5}x+\frac{16}{5} \\ y=\frac{4}{5}x+\frac{16}{5}-1 \\ y=\frac{4}{5}x+\frac{11}{5} \end{gathered}$

B) The same line described by the slope-intercept formula:

$\begin{gathered} y=\frac{4}{5}x+b \\ -1=\frac{4}{5}(-4)+b \\ -1=\frac{-16}{5}+b \\ -1=-\frac{16}{5}+b \\ -1+\frac{16}{5}=b \\ \frac{11}{5}=b \\ y=\frac{4}{5}x+\frac{11}{5} \end{gathered}$

C) Plugging into the function the y-coordinate: 7

$\begin{gathered} y=\frac{4}{5}x+\frac{11}{5} \\ 7=\frac{4}{5}x+\frac{11}{5} \\ 7-\frac{11}{5}=\frac{4}{5}x \\ \frac{24}{5}=\frac{4}{5}x\text{ }\times5 \\ 24=4x \\ \frac{24}{4}=\frac{4x}{4} \\ 6=x \\ x=6 \end{gathered}$

The x-coordinate for y=7 is x= 6.

That's the function y=4/5x +11/5