Question

Write an equation in point-slope form of the line that passes through the two given points. Use the first point to write the equation (-1, -5) and (3, 2)

Answer 1

Answer:

The equation in point-slope form of the line is:

$y-\left(-5\right)=\frac{7}{4}\left(x-\left(-1\right)\right)$

Step-by-step explanation:

Given the points

• (-1, -5)

• (3, 2)

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-1,\:-5\right),\:\left(x_2,\:y_2\right)=\left(3,\:2\right)$

$m=\frac{2-\left(-5\right)}{3-\left(-1\right)}$

$m=\frac{7}{4}$

As the point-slope form is defined as

$y-y_1=m\left(x-x_1\right)$

where m is the slope.

substituting the values m=7/4 and the first point (-1, -5)

$y-\left(-5\right)=\frac{7}{4}\left(x-\left(-1\right)\right)$

Therefore, the equation in point-slope form of the line is:

$y-\left(-5\right)=\frac{7}{4}\left(x-\left(-1\right)\right)$