a We have been given the vertices of a triangle as the following.
A(0,0), B(2,5), C(4,0)
Let's plot the points and draw the triangle to have a better understanding.
In order to write an equation for the line that passes through the points A and B, we will first determine the slope of the line. We will use the formula to determine the Slope Formula.
m=rise/run=y_2- y_1/x_2- x_1
In the formula, (x_1,y_1) and (x_2,y_2) are the points that are on the line. Let's apply the formula!
The slope of the line is 52. We also know that the y-intercept of the line is because it passes through A(0,0). Thus, we will write the equation in slope-intercept form.
y=5/2x
b This time, we will write an equation of the line that passes through the points B and C in the same way.
The slope of the line is - 52. This time, we will write the equation in point-slope form because we do not know its y-intercept. Let's use the point C as our point.
y-0=-5/2(x-4)
Let's distribute - 52 so that we have the equation in slope-intercept form.
y=-5/2x+10
c The absolute value of the slopes are the same. However, one of the lines has a positive slope and the other has a negative slope. The y-intercept of the line from Part A is and the line from Part B is 10.
