How do you write an equation in slope intercept form given that the line passes through the points (4,1) and (2,-3)?

Question

How do you write an equation in slope intercept form given that the  line passes through the points (4,1) and (2,-3)?

Abigail Allen · Accepted Answer

First we have to find the slope of the equation. To find the slope we have to do;
#(y2-y1)/(x2-x1)# For our question slope is;

#(-3-1)/(2-4) = (-4)/-2 = 2#

The main formula of a line is;
#y=ax+b#

We should use one point to find the real equation. If we use (4,1) point;
#y= ax+b => 1=4a+b#;
a is the slope of the equation, we found that as #2#;
#1=(4*2) + b => 1=8 +b => b=-7#;
So the equation of the line will be;
#y=ax+b => ul (y= 2x-7)#
We can check if our equation is right or not with other given point;
#(2,-3) => y=2x-7 => -3=2*2-7 => -3=4-7 => -3=-3 #

Savannah Anderson · Answer

undefined To write an equation in slope-intercept form (y = mx + b) given that the line passes through the points (4,1) and (2,-3):

1. Calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) = (4,1) and (x2, y2) = (2,-3).
2. Once you have the slope (m), choose one of the points (either (4,1) or (2,-3)) and substitute the coordinates into the equation y = mx + b to solve for the y-intercept (b).
3. After finding the slope (m) and the y-intercept (b), write the equation in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.