Question

Find the slope of the line that contains the points named a (o,d),b (d,o)

Answer 1

Answer:

-1

Step-by-step explanation:

Hello,

The slope is the inclination of the line with respect to the abscissa axis, if you know two points  it can be calculated using:

$P1(x_{1},y_{1} )\\P2(x_{2},y_{2} )\\\\slope(m)=\frac{y_{2} -y_{1} }{x_{2}-x_{1}}$

Step 1

Define

$P1=a(o,d),x_{1} =o, y_{1}=d \\P2=b(d,o),x_{2} =d, y_{2}=o$

Step 2

put the values into the equation

$slope(m)=\frac{y_{2} -y_{1} }{x_{2}-x_{1}}\\slope(m)=\frac{o-d}{d-o}\\factorize -1\\\\slope(m)=-\frac{-o+d}{d-o}\\slope(m)=-\frac{d-o}{d-o}\\slope(m)=-1$

Have a great day

Answer 2

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ d}})\quad % (c,d) &({{ d}}\quad ,&{{ 0}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{0-d}{d-0}\implies \cfrac{-d}{d}\implies -1$