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 \(-9x+2y=53\)
