+2440 Before attempting to do this problem, you must understand the slope-intercept form of a line. It is the following:
\(y=mx+b\)
m = slope of the line
b = the y-intercept (the point where it touches the y-axis)
First, we must find the slope. To do this, we must know another formula. This will solve for m.
\(m=\frac{y_2-y_1}{x_2-x_1}\)
Now that we know the formula, let's plug the given coordinates into the formula above to determine the line's slope:
| \(m=\frac{y_2-y_1}{x_2-x_1}\) | Plug in the coordinate given into this formula to find the slope of the line, |
| \(m=\frac{4-(-3)}{3-8}\) | Remember that subtracting a negative is the same as adding a positive. |
| \(m=\frac{4+3}{3-8}\) | Now, simplify the numerator and denominator into its simplest terms. |
| \(m=\frac{7}{-5}=-\frac{7}{5}\) | |
We have now determined the slope of the line, -7/5. The next step is to figure out the value of b. First, let's look at the equation with the m filled in.
\(y=-\frac{7}{5}x+b\)
Just plug in a coordinate into here and solve for b. It doesn't matter which coordinate you substitute in, either. I'll use the first point, (3,4):
| \(y=-\frac{7}{5}x+b\) | Plug in the coordinate (3,4) into the equation and solve for b. |
| \(4=-\frac{7}{5}*3+b\) | First, let's simplify the right hand side of the equation by doing -7/5*3 |
| \(-\frac{7}{5}*3=\frac{-7}{5}*\frac{3}{1}=\frac{-21}{5}=-\frac{21}{5}\) | Plug this back into the equation we were solving. |
| \(4=-\frac{21}{5}+b\) | Multiply 5 on both sides of the equation to get rid of the pesky fractions. |
| \(20=-21+5b\) | Add 21 to both sides of the equation. |
| \(41=5b\) | Divide by 5 on both sides. |
| \(\frac{41}{5}=b\) | |
Now that we have both m and b solved, we can write the equation in slope intercept form.
\(y=mx+b\)
Just replace m and b with the numbers we calculated for both. Therefore, your final answer is:
\(y=-\frac{5}{7}x+\frac{41}{5}\)
Here, I have supplied a link to an online graphing calculator called Desmos. It shows you that this is indeed the line that passes through both points. Here is the link: https://www.desmos.com/calculator/0tjwjbb3e7
