Graph Calculator

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Graph Calculator: Linear Equation & Coordinates
Find Equation from Two Points (x1, y1) and (x2, y2)Find Line Properties from Slope (m) and Intercept (b)
Analysis Result:
Enter coordinates to see the graph equation.
function calculateResult(){var type=document.getElementById('calc_type').value;var v1=parseFloat(document.getElementById('val1').value);var v2=parseFloat(document.getElementById('val2').value);var v3=parseFloat(document.getElementById('val3').value);var v4=parseFloat(document.getElementById('val4').value);var ans=document.getElementById('answer');var showSteps=document.getElementById('steps').checked;if(type==='two_points'){if(isNaN(v1)||isNaN(v2)||isNaN(v3)||isNaN(v4)){ans.innerHTML='Error: Please enter all four coordinate values.';return;}if(v1===v3){ans.innerHTML='Equation: x = '+v1+'
Slope: Undefined (Vertical Line)
Distance: '+Math.abs(v4-v2).toFixed(4);return;}var m=(v4-v2)/(v3-v1);var b=v2-(m*v1);var dist=Math.sqrt(Math.pow(v3-v1,2)+Math.pow(v4-v2,2));var midX=(v1+v3)/2;var midY=(v2+v4)/2;var sign=b>=0?'+ ':'- ';var bAbs=Math.abs(b).toFixed(4);var res='
';res+='Slope (m): '+m.toFixed(4)+'
';res+='Y-Intercept (b): '+b.toFixed(4)+'
';res+='Line Equation: y = '+m.toFixed(4)+'x '+sign+bAbs+'
';res+='Distance: '+dist.toFixed(4)+'
';res+='Midpoint: ('+midX+', '+midY+')';if(showSteps){res+='
Steps:
';res+='1. m = (y₂ – y₁) / (x₂ – x₁) = ('+v4+' – '+v2+') / ('+v3+' – '+v1+') = '+m.toFixed(4)+'
';res+='2. b = y₁ – m*x₁ = '+v2+' – ('+m.toFixed(4)+'*'+v1+') = '+b.toFixed(4);}res+='
';ans.innerHTML=res;}else{if(isNaN(v1)||isNaN(v2)){ans.innerHTML='Error: Please enter Slope (m) and Intercept (b).';return;}var xInt=-v2/v1;var res='
';res+='Equation: y = '+v1+'x + '+v2+'
';res+='Slope: '+v1+'
';res+='Y-Intercept: (0, '+v2+')
';res+='X-Intercept: ('+xInt.toFixed(4)+', 0)';res+='
';ans.innerHTML=res;}}document.getElementById('calc_type').onchange=function(){var t=this.value;if(t==='two_points'){document.getElementById('label1′).innerHTML='x₁ Coordinate:';document.getElementById('label2′).innerHTML='y₁ Coordinate:';document.getElementById('label3′).innerHTML='x₂ Coordinate:';document.getElementById('label4′).innerHTML='y₂ Coordinate:';document.getElementById('val3′).parentElement.parentElement.style.display='table-row';document.getElementById('val4′).parentElement.parentElement.style.display='table-row';}else{document.getElementById('label1′).innerHTML='Slope (m):';document.getElementById('label2′).innerHTML='Y-Intercept (b):';document.getElementById('val3′).parentElement.parentElement.style.display='none';document.getElementById('val4′).parentElement.parentElement.style.display='none';}};

Using the Graph Calculator

The graph calculator is a specialized tool designed to help you analyze linear relationships on a Cartesian plane. Whether you are a student solving algebra homework or a professional needing to find the distance between two points, this tool provides instant results for slopes, intercepts, and full linear equations.

This tool supports two primary modes of calculation:

Two-Point Mode
Enter the (x, y) coordinates for two distinct points. The calculator finds the slope, the y-intercept, the total distance between the points, and the midpoint.
Slope-Intercept Mode
Enter the known slope (m) and y-intercept (b) to generate the standard line equation and find the x-intercept where the graph crosses the horizontal axis.

How It Works: The Math Behind the Graph

Every straight line on a graph follows a mathematical pattern. The most common way to express this is the Slope-Intercept Form:

y = mx + b

Our graph calculator uses the following formulas to derive your results:

  • Slope (m): Calculated as the "rise over run" or (y₂ – y₁) / (x₂ – x₁).
  • Y-Intercept (b): The point where x = 0. Found using b = y₁ – m(x₁).
  • Distance: Found using the Pythagorean theorem variant: √[(x₂ – x₁)² + (y₂ – y₁)²].
  • Midpoint: The center point between two coordinates, calculated as ((x₁ + x₂) / 2, (y₁ + y₂) / 2).

Calculation Example

Example: Suppose you have two points on a graph: Point A at (1, 2) and Point B at (4, 8). You want to find the equation of the line that passes through them.

Step-by-step solution:

  1. Find Slope (m): (8 – 2) / (4 – 1) = 6 / 3 = 2
  2. Find Y-Intercept (b): 2 = 2(1) + b → 2 = 2 + b → b = 0
  3. Line Equation: y = 2x + 0 (or simply y = 2x)
  4. Distance: √[(4-1)² + (8-2)²] = √[3² + 6²] = √[9 + 36] = √45 ≈ 6.708

Common Questions

What is a "negative" slope?

A negative slope means the line goes "downhill" from left to right. As the x-value increases, the y-value decreases. In our graph calculator, this will appear as a negative number for 'm'.

What happens if the x-coordinates are the same?

If x₁ equals x₂, the "run" (denominator) is zero. Since division by zero is impossible, the slope is undefined. This represents a perfectly vertical line, and its equation is written as x = [value].

Can this calculator handle fractions?

Yes, you can enter decimal approximations for fractions (e.g., 0.5 for 1/2). The graph calculator will process these values and provide highly accurate outputs for your coordinates.

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