Answer:
[tex]y=\frac{9}{2}x+[tex]\frac{53}{2}[/tex]
[tex]9x-2y=-53[/tex]
Step-by-step explanation:
The line is passing through [tex](-7,-5)[/tex] and [tex](-5,4)[/tex].
The equation of line in point-slope form can be obtained by using the following rule that says:
[tex](y-y_1)=m(x-x_1)[/tex]
Lets say: [tex](x_1,y_1),(x_2,y_2)[/tex] are [tex](-7,-5)[/tex] and [tex](-5,4)[/tex] respectively.
Lets find the slope of the line:
[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{4-(-5)}{-5-(-7)} =\frac{4+5}{-5+7}=\frac{9}{2}[/tex]
So the slope of the line is [tex]\frac{9}{2}[/tex].
[tex](y-(-5))=\frac{9}{2}(x-(-7))[/tex]
[tex]y+5=\frac{9}{2}(x+7)[/tex]
[tex]y=\frac{9}{2}x+[tex]\frac{9}{2}\times 7[/tex]-5=\frac{9}{2}x+[tex]\frac{53}{2}[/tex]
[tex]y=\frac{9}{2}x+[tex]\frac{53}{2}[/tex]
So the required equation is [tex]y=\frac{9}{2}x+[tex]\frac{53}{2}[/tex].
And the equation of line in standard form can be written as:
[tex]\frac{-9}{2}x+y=[tex]\frac{53}{2}[/tex]
Multiplying the equation by 2 we get:
[tex]-9x+2y=53[/tex]
[tex]9x-2y=-53[/tex]
Answer:
The point-slope form is [tex]y+5=\frac{9}{2} (x+7)[/tex].
The standard form of a line is [tex]-9x + 2y = 53[/tex].
Step-by-step explanation:
Point-slope is a specific form of linear equations in two variables:
[tex]y-b=m(x-a)[/tex]
When an equation is written in this form, [tex]m[/tex] gives the slope of the line and [tex](a,b)[/tex] is a point the line passes through.
To find the line that passes through the points [tex](-7, -5)[/tex] and [tex](-5, 4)[/tex]. First, we use the two points to find the slope:
[tex]m=\frac{4-(-5)}{-5-(-7)} =\frac{9}{2}[/tex]
Now we use one of the points, let's take [tex](-7, -5)[/tex], and write the equation in point-slope:
[tex]y+5=\frac{9}{2} (x+7)[/tex]
The standard form of a line is in the form [tex]Ax + By = C[/tex] where A is a positive integer, and B, and C are integers.
To find this form you must
[tex]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[/tex]
