Question

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

Answer 1

Answer:

$y=\frac{9}{2}x+[tex]\frac{53}{2}$

$9x-2y=-53$

Step-by-step explanation:

The line is passing through $(-7,-5)$ and $(-5,4)$.

The equation of line in point-slope form can be obtained by using the following rule that says:

$(y-y_1)=m(x-x_1)$

Lets say: $(x_1,y_1),(x_2,y_2)$ are $(-7,-5)$ and $(-5,4)$ respectively.

Lets find the slope of the line:

$m=\frac{y_2-y_1}{x_2-x_1} =\frac{4-(-5)}{-5-(-7)} =\frac{4+5}{-5+7}=\frac{9}{2}$

So the slope of the line is $\frac{9}{2}$.

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

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

$y=\frac{9}{2}x+[tex]\frac{9}{2}\times 7$-5=\frac{9}{2}x+$\frac{53}{2}$

$y=\frac{9}{2}x+[tex]\frac{53}{2}$

So the required equation is $y=\frac{9}{2}x+[tex]\frac{53}{2}$.

And the equation of line in standard form can be written as:

$\frac{-9}{2}x+y=[tex]\frac{53}{2}$

Multiplying the equation by 2 we get:

$-9x+2y=53$

$9x-2y=-53$

Answer 2

Answer:

The point-slope form is $y+5=\frac{9}{2} (x+7)$.

The standard form of a line is $-9x + 2y = 53$.

Step-by-step explanation:

Point-slope is a specific form of linear equations in two variables:

$y-b=m(x-a)$

When an equation is written in this form, $m$ gives the slope of the line and $(a,b)$ is a point the line passes through.

To find the line that passes through the points $(-7, -5)$ and $(-5, 4)$. First, we use the two points to find the slope:

$m=\frac{4-(-5)}{-5-(-7)} =\frac{9}{2}$

Now we use one of the points, let's take $(-7, -5)$, and write the equation in point-slope:

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

The standard form of a line is in the form $Ax + By = C$ where A is a positive integer, and B, and C are integers.

To find this form you must

$y+5=\frac{9}{2} (x+7)\\\\y+5-5=\frac{9}{2}\left(x+7\right)-5\\\\y=\frac{53}{2}+\frac{9}{2}x\\\\2y=9x+53\\\\-9x+2y=53$