Finding the Equation of a Line Given Two Points

  • MHB
  • Thread starter mathdad
  • Start date
In summary, to find an equation of the line passing through (6, -3) and having a y-intercept of 8, we can use the slope-intercept formula y = mx + b, where b represents the y-intercept. Since 8 is given to be the y-intercept, it can be written as (0, 8). We can then find the slope m by using the points (6, -3) and (0, 8), and plugging them into the formula m = (y2 - y1) / (x2 - x1). Once we have the slope, we can use the point-slope formula and plug in the values for m and b to isolate y and find
  • #1
mathdad
1,283
1
Find an equation of the line that passes through (6, -3) and has y-intercept 8.

I know y = mx + b is the slope-intercept formula. In the formula, b represents the y-intercept. I also see that 8 is given to be b in this case.

The y-intercept can be written as (0, 8).

Do I now find the slope m?
Afterward, use one of the points and m to plug into the point-slope formula. Finally, I must isolate y.

Is this right?
 
Mathematics news on Phys.org
  • #2
Like you, I would begin with the slope-intercept form of a line:

\(\displaystyle y=mx+b\)

We are given $b=8$, and we know two points on the line, so we can compute the slope $m$:

\(\displaystyle m=\frac{8-(-3)}{0-6}=\)?

Then, just plug in the values for $m$ and $b$. :)
 
  • #3
MarkFL said:
Like you, I would begin with the slope-intercept form of a line:

\(\displaystyle y=mx+b\)

We are given $b=8$, and we know two points on the line, so we can compute the slope $m$:

\(\displaystyle m=\frac{8-(-3)}{0-6}=\)?

Then, just plug in the values for $m$ and $b$. :)

I can take it from here. Thanks.
 

FAQ: Finding the Equation of a Line Given Two Points

What is the equation of a line?

The equation of a line is a mathematical representation that describes the relationship between two variables, typically written in the form y = mx + b. The variables represent the y-coordinate, slope, and y-intercept, respectively.

How do you find the equation of a line?

To find the equation of a line, you need to know at least two points on the line. You can then use the slope formula (m = (y2 - y1)/(x2 - x1)) to calculate the slope, and plug the slope and one of the points into the slope-intercept form (y = mx + b) to solve for the y-intercept.

What is slope?

Slope is a measure of the steepness of a line. It is calculated by dividing the change in the y-coordinate by the change in the x-coordinate between two points on the line. A positive slope indicates an upward trend, while a negative slope indicates a downward trend.

What is the y-intercept?

The y-intercept is the point where the line crosses the y-axis. In the equation y = mx + b, the y-intercept is represented by the b term. It indicates the value of the y-coordinate when the x-coordinate is 0.

Can the equation of a line be written in different forms?

Yes, the equation of a line can also be written in the point-slope form (y - y1 = m(x - x1)) or the standard form (Ax + By = C). These forms may be more useful in certain situations, such as when solving systems of equations or graphing lines on a coordinate plane.

Back
Top