Answer:
Option C is correct
[tex]y+5 = \frac{9}{2}(x+7)[/tex]
[tex]-9x+2y=53[/tex]
Step-by-step explanation:
Point slope form:
The equation of line is given by:
[tex]y-y_1=m(x-x_1)[/tex] ....[1] where m is the slope and a point [tex](x_1, y_1)[/tex] lies on the line.
Given that:
A line passes through (-7,-5) and (-5,4).
Calculate slope:
Slope is given by:
[tex]\text{Slope} = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given values we have;
[tex]\text{Slope (m)} = \frac{4-(-5)}{-5-(-7)}[/tex]
Simplify:
[tex]m = \frac{9}{2}[/tex]
Substitute thee value of m and (-7, -5) in [1] we have;
[tex]y-(-5)=\frac{9}{2}(x-(-7))[/tex]
Simplify:
[tex]y+5 = \frac{9}{2}(x+7)[/tex]
⇒[tex]2(y+5) = 9(x+7)[/tex]
Using distributive property :[tex]a \cdot(b+c) = a\cdot b+ a\cdot c[/tex]
[tex]2y+10=9x+63[/tex]
Subtract 9x from both sides we have;
[tex]-9x+2y+10=63[/tex]
Subtract 10 from both sides we have;
[tex]-9x+2y=53[/tex]
Therefore, an equation for the line in point-slope form is [tex]y+5 = \frac{9}{2}(x+7)[/tex] and the equation in standard form using integers is [tex]-9x+2y=53[/tex]
