There are two approaches to solving this problem: (a) using the slope-intercept form of the linear equation, and (b) using the definition of the y-intercept.
First, recall the slope-intercept form, y = mx + b where m is the slope and x is the y-intercept. Let's transform the given equation to this form:
13x - 15y = 20
- 15y = - 13x + 20
y = (13/15)*x - 20/15
.: y = (13/15)*x - 4/3
Thus, the y - intercept is -4/3.
Alternatively, recall that the y-intercept is the y-coordinate of the point where the line crosses the y-axis. This means that the point has a zero x-intercept since it lies on the y-axis. Hence, this point has the coordinates: (0,b) where b is the y-intercept.
Solve for b which is the y-intercept:
13x - 15y = 20
13(0) - 15y = 20
-15y = 20
y = -4/3
.: b = -4/3
Hence we say that the y-intercept of the line 13x - 15y = 20 is -4/3.
Answers & Comments
Verified answer
The best way to find the slope and the y intercept is to put the equation into the slope, y-intercept form.
This is y = mx + b
When the equation of a line is in this form, the slope is the value at m and the y intercept is the value at b.
So solve the equation for y to put it in the slope, y-intercept form.
Given 13x - 15y = 20, solve for y
1) Subtract 13x from both sides
- 15y = - 13x + 20
2) Divide all the terms on both sides by - 15
y = (+13 / 15 )x - 20 / 15
3) Reduce the fraction
y = ( 13 / 15 )x - 4 / 3
ANSWER:
The slope is the value at m, which in this case is 13/15
The y intercept is the value at b, which in this case is - 4 / 3
There are two approaches to solving this problem: (a) using the slope-intercept form of the linear equation, and (b) using the definition of the y-intercept.
First, recall the slope-intercept form, y = mx + b where m is the slope and x is the y-intercept. Let's transform the given equation to this form:
13x - 15y = 20
- 15y = - 13x + 20
y = (13/15)*x - 20/15
.: y = (13/15)*x - 4/3
Thus, the y - intercept is -4/3.
Alternatively, recall that the y-intercept is the y-coordinate of the point where the line crosses the y-axis. This means that the point has a zero x-intercept since it lies on the y-axis. Hence, this point has the coordinates: (0,b) where b is the y-intercept.
Solve for b which is the y-intercept:
13x - 15y = 20
13(0) - 15y = 20
-15y = 20
y = -4/3
.: b = -4/3
Hence we say that the y-intercept of the line 13x - 15y = 20 is -4/3.
slope dy/dx=13/15
y-intercept y=-4/3
x=0
slope: -13/15
y-intercept: -4/3 or -1 1/3
13x-15y=20
-13x -13x
----------------------
-15y=-13x+20
----- ----- ----
-15 -15 -15
y=-13/15x-20/15
Slope: 13/15; Y-Int: -20/15
y=13/15x-20
y intercept is 20
slope is 13/15
im not sure