Answer:
Point-Slope form:
y - 5 = -1(x - 2)
or, Slope-Intercept:
y = -x + 7
or, Standard form:
x + y = 7
Explanation:
In order to write the equation of a line in Point-Slope form you just need a point and the slope. You have two points so you can calculate the slope (and use either point)
For the slope, subtract the y's and put that on top of a fraction. 5 - 3 is 2, put it on top.
Subtract the x's and put that on the bottom of the fraction. 2 - 4 is -2, put that on the bottom of the fraction. 2/-2 is the slope; let's simplify it.
2/-2
= -1
The slope is -1.
Lets use Point-Slope formula, which is a fill-in-the-blank formula to write the equation of a line:
y - Y = m(x - X)
fill in either of your points for the X and Y, and fill in slope for m. Slope is -1 and X and Y can be (2,5)
y - Y = m(x -X)
y - 5 = -1(x - 2)
This is the equation of the line in Point-Slope form. Solve for y to change it to Slope-Intercept form.
y - 5 = -1(x - 2)
use distributive property
y - 5 = -x + 2
add 5 to both sides
y = -x + 7
This is the equation of the line in Slope-Intercept Form.
Standard Form is:
Ax + By = C
y = -x + 7
add x to both sides
x + y = 7
This is the equation in Standard Form.