Question

I need to know the answer this, please and thank you it’s past my bed time lol

Answer 1

Answer:

To find the slope-intercept equation of a line, we need the slope (m) and the y-intercept (b).

The slope-intercept equation is noted as:

$y=mx+b$

To find the slope, we will use the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Line 1:

The line passes through the points (-1, -4) and (1, 2). Using these points, we will solve the slope:

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

Then, using the point (-1, -4), we will solve for b:

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

Now that we have the values of slope (m) and y-intercept (b), we now know that the slope-intercept form of line 1 is:

$\begin{gathered} y=mx+b \\ y=3x-1 \end{gathered}$

Line 2:

Following the same process, we will find the slope (m), then the y-intercept (b).

Line 2 passes through points (-4, 0) and (0,4)

$\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{4-0}{0-(-4)} \\ m=\frac{4}{0+4} \\ m=\frac{4}{4}=1 \end{gathered}$

Then solve for the y-intercept (b) using the point (-4, 0):

$\begin{gathered} y=mx+b \\ 0=-4+b \\ b=4 \end{gathered}$

The equation would then be:

$\begin{gathered} y=mx+b \\ y=x+4 \end{gathered}$

Line 3:

Line 3 passes through points (1, 0) and (0,2)

$\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{2-0}{0-1} \\ m=\frac{2}{-1}=-2 \end{gathered}$$\begin{gathered} y=mx+b \\ 0=-2(1)+b \\ 0=-2+b \\ b=2 \end{gathered}$

The equation then would be:

$\begin{gathered} y=mx+b \\ y=-2x+2 \end{gathered}$

Line 4:

Line 4 passes through points (-2, 3) and (2, 1)

$\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{1-3}{2-(-2)} \\ m=\frac{-2}{4}=-\frac{1}{2} \end{gathered}$$\begin{gathered} y=mx+b \\ 3=-\frac{1}{2}(-2)+b \\ 3=1+b \\ b=3-1 \\ b=2 \end{gathered}$

The equation is then:

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

With all these, we can write each line's corresponding letter:

Line 1: A

Line 2: E

Line 3: B

Line 4: G