Slope Calculator
The slope of a line is a fundamental concept in mathematics and physics, representing the steepness or inclination of a line on a coordinate plane. It's often denoted by the letter 'm'. The slope quantifies how much the y-coordinate changes for every unit change in the x-coordinate.
Understanding Slope
The formula for calculating slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
In simpler terms, the slope is the "rise" (change in y) divided by the "run" (change in x).
- Positive Slope: Indicates a line that rises from left to right.
- Negative Slope: Indicates a line that falls from left to right.
- Zero Slope: Indicates a horizontal line (y1 = y2).
- Undefined Slope: Indicates a vertical line (x1 = x2).
Example Calculation:
Let's calculate the slope between two points: Point A (2, 3) and Point B (5, 7).
- x1 = 2, y1 = 3
- x2 = 5, y2 = 7
Using the formula:
m = (7 - 3) / (5 - 2)
m = 4 / 3
Therefore, the slope of the line connecting these two points is 4/3 or approximately 1.33.
function calculateSlope() {
var x1 = parseFloat(document.getElementById("x1").value);
var y1 = parseFloat(document.getElementById("y1").value);
var x2 = parseFloat(document.getElementById("x2").value);
var y2 = parseFloat(document.getElementById("y2").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(x1) || isNaN(y1) || isNaN(x2) || isNaN(y2)) {
resultDiv.innerHTML = "Please enter valid numbers for all coordinates.";
return;
}
var deltaY = y2 – y1;
var deltaX = x2 – x1;
if (deltaX === 0) {
if (deltaY === 0) {
resultDiv.innerHTML = "The points are identical. Slope is indeterminate.";
} else {
resultDiv.innerHTML = "The slope is
Undefined (vertical line).";
}
} else {
var slope = deltaY / deltaX;
var slopeString = slope.toFixed(4); // Format to 4 decimal places
var slopeDescription = "";
if (slope > 0) {
slopeDescription = "positive";
} else if (slope < 0) {
slopeDescription = "negative";
} else {
slopeDescription = "zero";
}
resultDiv.innerHTML = "The change in Y (rise) is: " + deltaY + "" +
"The change in X (run) is: " + deltaX + "" +
"The slope (m) is:
" + slopeString + " (" + slopeDescription + " slope).";
}
}
.slope-calculator-wrapper {
font-family: sans-serif;
border: 1px solid #ccc;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
background-color: #f9f9f9;
}
.slope-calculator-wrapper h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.inputs-section {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(150px, 1fr));
gap: 15px;
margin-bottom: 20px;
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.input-group input {
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
}
.inputs-section button {
grid-column: 1 / -1;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 1.1em;
transition: background-color 0.3s ease;
}
.inputs-section button:hover {
background-color: #0056b3;
}
.results-section {
margin-top: 20px;
padding: 15px;
background-color: #e9ecef;
border: 1px solid #ddd;
border-radius: 4px;
text-align: center;
}
.results-section p {
margin: 8px 0;
font-size: 1.1em;
}
.explanation-section {
margin-top: 30px;
border-top: 1px solid #eee;
padding-top: 20px;
}
.explanation-section h3 {
color: #333;
margin-bottom: 15px;
}
.explanation-section p, .explanation-section ul {
line-height: 1.6;
color: #444;
}
.explanation-section code {
background-color: #e0e0e0;
padding: 2px 5px;
border-radius: 3px;
}
.explanation-section ul {
margin-left: 20px;
}