Find The X And Y Intercepts Of A Line Using Algebra

The Algebra of Lines: Find the X and Y Intercepts of a Line Using Algebra

When the equation is written in the slope-intercept form (y=mx+b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.

To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis.

When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.

Video Source (08:37 mins) | Transcript

To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).

Additional Resources

• Khan Academy: Introduction to Intercepts (06:32 mins, Transcript)
• Khan Academy: X-intercept of a Line (01:42 mins, Transcript)
• Khan Academy: Intercepts from an Equation (04:07 mins, Transcript)

Practice Problems

1. Find the y-intercept of the line:\({\text{y}}=-3{\text{x}}-9\)
2. Find the x-intercept of the line:\({\text{y}}=-4{\text{x}}+12\)
3. Find the y-intercept of the line:y − 9 = 3x
4. Find the x-intercept of the line:y + 12 = 2x
5. Find the y-intercept of the line:\({\text{x}}+6{\text{y}}=-24\)
6. Find the x-intercept of the line:\(5{\text{x}}+4{\text{y}}=-20\)

View Solutions

Solutions

1. \({\text{y}}=-9\)
2. x = 3
3. y = 9 (Written Solution)

   Written solution: To find y-intercept: set x = 0 and solve for y. The point will be (0,y):

   y − 9 = 3x

   Substitute 0 in for x:

   y − 9 = 3 (0)

   Multiply 3 times 0, which gives us:

   y − 9 = 0

   Then add 9 to both sides to isolate y:

   y − 9 + 9 = 0 + 9

   Which gives us:

   y = 9

   So the y-intercept is (0,9)

4. x = 6
5. \({\text{y}}=-4\)
6. \({\text{x}}=-4\)(Written Solution)

   To find x-intercept: set y = 0 and solve for x. The point will be (x,0):

   \(5{\text{x}}+4{\text{y}}=-20\)

   Substitute 0 in for y:

   \(5{\text{x}}+4{\color{Red}(0)}=-20\)

   Multiply 4 times 0 which gives us:

   \(5{\text{x}}+{\color{Red}0}=-20\)

   Add 5x to 0:

   \(5{\text{x}}=-20\)

   Then multiply both sides by \(\frac{1}{5}\) (or divide both sides by 5, both will give you the same solution):

   \(\frac{1}{5}(5{\text{x}})\) = \(-20\frac{1}{5}\)

   Which gives us:

   \({\text{x}}=-4\)

   So they x-intercept is \((-4,0)\)