Question

Write the equation of the line that satisfies the following conditions:

Answer 1

Answer:

a. $y=-x+-5$

b. $y=\frac{4}{3}x+\frac{5}{3}$

Step-by-step explanation:

to solve part a we have the slope of the line and a point, so we use the point-slope equation

$y=m(x-x_{1})+y_{1}$

where $m$ is the slope: $m=-1$, and $(x_{1},y_{1})$ is the point, so in this case the point is $(0,-5)$ thus $x_{1}=0$ and $y_{1}=-5$.Thus the equation is:

$y=-1(x-0)+(-5)$

$y=-x+-5$

And for part b we have two points. With the two points we can find the slope and then use the point-slope equation again.

To find the slope we use:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

for the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$. Since we have the poits: $(1,3)$ and $(-2,-1)$

$x_{1}=1\\y_{1}=3\\x_{2}=-2\\y_{2}=-1$

Thus, the slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-1-3}{-2-1}$

$m=\frac{-4}{-3}$

$m=\frac{4}{3}$

and now using the point-slope equation:

$y=m(x-x_{1})+y_{1}$

$y=\frac{4}{3}(x-1)+3\\y=\frac{4}{3}x-\frac{4}{3} +3\\y=\frac{4}{3}x+\frac{5}{3}$