Question

oint - slope formula to write an equation of the line that passes through $(-3, -4)$ and $(4, 5)$. answer in slope - intercept form (if possible). quation of the line is

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(-3,-4)$ and $(x_2,y_2)=(4,5)$:
$m=\frac{5-(-4)}{4-(-3)}=\frac{9}{7}$

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Use $(x_1,y_1)=(-3,-4)$:
$y-(-4)=\frac{9}{7}(x-(-3))$
Simplify to $y+4=\frac{9}{7}(x+3)$

Step3: Convert to slope-intercept form

Expand and solve for $y$:
$y+4=\frac{9}{7}x+\frac{27}{7}$
$y=\frac{9}{7}x+\frac{27}{7}-4$
$y=\frac{9}{7}x+\frac{27}{7}-\frac{28}{7}$
$y=\frac{9}{7}x-\frac{1}{7}$

Answer:

$y=\frac{9}{7}x-\frac{1}{7}$