Solve Intercept Problems

Introduction for intercept:

The y-intercept is the y-value of the point where the graph of a function intercepts the y-axis of the coordinate system. The slope of a line describes its steepness, incline. A higher slope value indicates a steeper incline. Given two points (x1, y1) and (x2, y2) on a line, the slope m of the line is

The slope intercept form y = mx + b

Where,

Slope (m) =` (y_2 - y_1)/(x_2 - x_1)`

b - y slope intercept

Source: Wikipedia

Let us solve the intercept example problems and practice problems are given below.

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Example Problems for Intercept:

Example problem 1:

Solve for the y intercept and slope of the line, 7x - 28y = 14

Solution:

The slope intercept form is y = mx + b, where m is the slope of the line.

Given equation is in the form of ax + bx = c  To find the y- intercept Plug x = 0 in the equation

Here y intercept, so x = 0

7(0) - 28y = 14

0 - 28y = 14

-28y = 14

Divided by -28 on both sides,

`(-28y)/(-28)` = ` 14/(-28)`

After simplify this, we get

y = `-1/2`

y intercept = `-1/2`

Example problem 2:

Solve for the x intercept and slope of the line, 10x - 20y = 30

Solution:

The slope intercept form is y = mx + b, where m is the slope of the line.

Given equation is in the form of ax + bx = c  To find the x- intercept Plug y = 0 in the equation

Here x intercept, so y = 0

10x - 20(0) = 30

10x - 0 = 30

10x = 30

Divided by 10 on both sides,

` (10x)/(10)` = `(30)/(10)`

After simplify this, we get

x = 3

x intercept = 3

These example problems are helpful to study the intercept. Understanding 9th class syllabus is always challenging for me but thanks to all math help websites to help me out.

Practice Problems for Intercept:

Practice problem 1:

Solve for the x intercept and slope of the line, 20x - 10y = 40

Answer: x intercept = 2

Practice problem 2:

Solve for  the y intercept and slope of the line, 6x + 2y = 20

Answer: y intercept = 10