Y Intercept Formulas | List of Y Intercept Formulas You Should Know - BYJUS

# Y Intercept Formulas

The y-intercept of a linear equation is the point at which the graph of the equation crosses the y-axis. Here we will discuss the formula for the y-intercept as this calculation is essential to solve problems on lines and graphs....Read MoreRead Less

### The Y-intercept Formula

The y-intercept of a line is the value of the y-coordinate corresponding to which the value of the x-coordinate will be zero. We can determine the y-intercept of a line from its graph by observing the point at which the graph of the line intersects the y-axis. The value of the y-coordinate at this point of intersection is the y-intercept of the line.

We can determine the y-intercept of a line from its equation as well. The formula for the y-intercept of a straight line depends upon the form of the equation of the line.

If the equation of the line is in the standard form, that is, Ax + By = C, then the formula for the y-intercept is:

y = $$\frac{C}{B}$$ Where,

• y is the y-intercept
• B and C are the constants

If the equation of the line is in the slope-intercept form, that is,

y = mx + c, then, the y-intercept formula is:

y = c

Where,

• m = slope of the line
• c = y-intercept of the line

If the equation of the line is in the point-slope form, that is, y – b = m(x – a) then, the y-intercept formula is:

y = -am + b

Where,

• m is the slope of the line
• (a, b) are points on the line

### Solved Examples

Example 1: Find the y-intercept of the equation 5x + 2y = 12.

Answer: The given equation 5x + 2y = 12 is in the standard form.

So the y intercept is:

y = $$\frac{C}{B}$$      Formula for y-intercept

y = $$\frac{12}{2}$$     Substitute 12 for C and 2 for B

y = 6       Solve

Hence, the y-intercept is 6.

Example 2: Find the equation of the line in slope-intercept form with a slope of -3 and a y-intercept of 4.

Answer: As we have learned, a linear equation in the slope-intercept form is, y = mx + b

Here, the slope, m = -3 and y-intercept, b = 4

So, substituting these values in the slope-intercept equation form and by simplifying,

y = mx + b

= (-3)x + 4

y = -3x + 4

Hence, the equation of the line in slope-intercept form is y = -3x + 4

Example 3: Engineers are constructing a road that is 350 miles long. After 2 weeks, 150 miles of road still need to be constructed. How much time in total will it take to complete the road?

Answer: Let us write the equation of a line representing road length y (in miles) remaining after x weeks.

At the start of the construction, 350 miles needed to be constructed, that is, (0, 350). So the y-intercept is 350.

After 2 weeks, 150 miles still need to be constructed, that is, (2, 150).

Here, we have two points (0, 350) and (2, 150).

So the slope, m = $$\frac{\text{change in y}}{\text{change in x}}$$

m = $$\frac{-200}{2}=-100$$

So the equation of the line is y = -100x + 350

When the road is completed y = 0, that is,

0 = -100x + 350

-350 = -100x      [Subtract 350 from both sides]

3.5 = x               [Divide each side by -100]

Therefore it takes 3.5 weeks to complete the construction of the road.