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