Find the equation of the straight line that passes through S (-8, 13) and T (-20, 22).
Understand the Problem
The question is asking us to find the equation of a straight line that passes through the two given points S and T. This involves using the coordinates of points S (-8, 13) and T (-20, 22) to determine the slope of the line and then applying the point-slope form of a linear equation.
Answer
The equation of the straight line that passes through points S and T is: $$ y = -\frac{3}{4}x + 7 $$
Answer for screen readers
The equation of the straight line that passes through points S and T is: $$ y = -\frac{3}{4}x + 7 $$
Steps to Solve
- Calculate the Slope of the Line
The slope $m$ can be calculated using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Here, $(x_1, y_1)$ is the point S (-8, 13) and $(x_2, y_2)$ is the point T (-20, 22).
Substituting the values: $$ m = \frac{22 - 13}{-20 - (-8)} = \frac{9}{-12} = -\frac{3}{4} $$
- Use the Point-Slope Form
Now we will use the point-slope form of the line equation, which is: $$ y - y_1 = m(x - x_1) $$ Using point S (-8, 13): $$ y - 13 = -\frac{3}{4}(x + 8) $$
- Expand and Simplify
Expanding the equation: $$ y - 13 = -\frac{3}{4}x - 6 $$ Now, add 13 to both sides to get $y$ alone: $$ y = -\frac{3}{4}x + 7 $$
- Final Equation
The equation of the line passing through points S and T is: $$ y = -\frac{3}{4}x + 7 $$
The equation of the straight line that passes through points S and T is: $$ y = -\frac{3}{4}x + 7 $$
More Information
This equation represents a linear function where the slope indicates that for every four units moved to the right on the x-axis, the line moves three units down on the y-axis. The y-intercept at $7$ indicates where the line crosses the y-axis.
Tips
- Confusing the order of the points: Ensure that when calculating the slope, the coordinates are used correctly.
- Forgetting to simplify the slope or the final equation: Always check if your fractions can be reduced.
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