Question

A line passes through (-7,-5) and (-5,4). Write an equation for the line in point-slope form. Rewrite the equation in standard form using integers.
A. y+5= 9/2 (x-7); -9x+2y=53
B. y+7= 9/2 (x+5); -9x+2y=31
C. y+5= 9/2 (x+7); -9x+2y=53
D. y-5= 9/2 (x+7); -9x + 2y=-53

Answer 1

The equation:
y - y 1 =  ( y2 - y1 ) / ( x2- x1) * ( x - x1 )
y - ( - 5 ) = ( 4 + 5 ) / ( - 5 + 7 ) * ( x - ( - 7 ) )
y + 5 = 9/2 ( x + 7 )
y + 5 = 9/2 x + 63 /2  / * 2
2 y + 10 = 9 x + 63
- 9 x + 2 x = 53
Answer:
C ) y + 5 = 9/2 ( x + 7 ) ;   - 9 x + 2 y = 53

Answer 2

Answer:

Option C is correct

$y+5 = \frac{9}{2}(x+7)$

$-9x+2y=53$

Step-by-step explanation:

Point slope form:

The equation of line is given by:

$y-y_1=m(x-x_1)$     ....[1] where m is the slope and a point $(x_1, y_1)$ lies on the line.

Given that:

A line passes through (-7,-5) and (-5,4).

Calculate  slope:

Slope is given by:

$\text{Slope} = \frac{y_2-y_1}{x_2-x_1}$

Substitute the given values we have;

$\text{Slope (m)} = \frac{4-(-5)}{-5-(-7)}$

Simplify:

$m = \frac{9}{2}$

Substitute thee value of m and (-7, -5) in [1] we have;

$y-(-5)=\frac{9}{2}(x-(-7))$

Simplify:

$y+5 = \frac{9}{2}(x+7)$

⇒$2(y+5) = 9(x+7)$

Using distributive property :$a \cdot(b+c) = a\cdot b+ a\cdot c$

$2y+10=9x+63$

Subtract 9x from both sides we have;

$-9x+2y+10=63$

Subtract 10 from both sides we have;

$-9x+2y=53$

Therefore, an equation for the line in point-slope form is $y+5 = \frac{9}{2}(x+7)$ and the equation in standard form using integers is $-9x+2y=53$