Question

use the given conditions to write an equation for the line in point - slope form and slope - intercept form. passing through $(-3,-5)$ and $(2,5)$

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(-3,-5)$ and $(x_2,y_2)=(2,5)$:
$$m=\frac{5-(-5)}{2-(-3)}=\frac{10}{5}=2$$

Step2: Write point-slope form

Point-slope form is $y-y_1=m(x-x_1)$. Use $(x_1,y_1)=(-3,-5)$ and $m=2$:
$y-(-5)=2(x-(-3))$ which simplifies to $y+5=2(x+3)$
(Using the other point $(2,5)$ gives $y-5=2(x-2)$, which is also valid)

Step3: Convert to slope-intercept form

Expand the point-slope equation:
$y+5=2x+6$
Subtract 5 from both sides:
$y=2x+6-5$

Answer:

Point-slope form: $\boldsymbol{y+5=2(x+3)}$ (or $\boldsymbol{y-5=2(x-2)}$)
Slope-intercept form: $\boldsymbol{y=2x+1}$