There are no exponents on the variables There are only two variables, neither of which are fractions (for example, you would not have 1x{\displaystyle {\frac {1}{x}}} The equation can be simplified to the form y=mx+b{\displaystyle y=mx+b}, where m and b are constants (numbers like 3, 10, -12, 43,35{\displaystyle {\frac {4}{3}},{\frac {3}{5}}}). [2] X Research source
y=2x+6{\displaystyle y=2x+6} Slope = 2 y=2−x{\displaystyle y=2-x} Slope = -1 y=38x−10{\displaystyle y={\frac {3}{8}}x-10} Slope = 38{\displaystyle {\frac {3}{8}}} [3] X Research source
Find the slope of 2y−3=8x+7{\displaystyle 2y-3=8x+7} Set to the form y=mx+b{\displaystyle y=mx+b}: 2y−3+3=8x+7+3{\displaystyle 2y-3+3=8x+7+3} 2y=8x+10{\displaystyle 2y=8x+10} 2y2=8x+102{\displaystyle {\frac {2y}{2}}={\frac {8x+10}{2}}} y=4x+5{\displaystyle y=4x+5} Find the slope: Slope = M = 4[4] X Research source
2y−3+3=8x+7+3{\displaystyle 2y-3+3=8x+7+3} 2y=8x+10{\displaystyle 2y=8x+10} 2y2=8x+102{\displaystyle {\frac {2y}{2}}={\frac {8x+10}{2}}} y=4x+5{\displaystyle y=4x+5}
Slope = M = 4[4] X Research source
Positive slopes go higher the further right you go. Negative slopes go lower the further right you go. Bigger slopes are steeper lines. Small slopes are always more gradual. Perfectly horizontal lines have a slope of zero. Perfectly vertical lines do not have a slope at all. Their slope is “undefined. “[6] X Research source
In each pair, the x coordinate is the first number, the y coordinate comes after the comma. Each x coordinate on a line has an associated y coordinate.
x1: 2 y1: 4 x2: 6 y2: 6[9] X Research source
Original Points: (2,4) and (6,6). Plug into Point Slope: 6−46−2{\displaystyle {\frac {6-4}{6-2}}} Simplify for Final Answer: 24=12{\displaystyle {\frac {2}{4}}={\frac {1}{2}}} = Slope
Original Points: (2,4) and (6,6). Plug into Point Slope: 6−46−2{\displaystyle {\frac {6-4}{6-2}}} Simplify for Final Answer: 24=12{\displaystyle {\frac {2}{4}}={\frac {1}{2}}} = Slope
6−46−2{\displaystyle {\frac {6-4}{6-2}}}
24=12{\displaystyle {\frac {2}{4}}={\frac {1}{2}}} = Slope
Review taking derivatives here The most simple derivatives, those for basic polynomial equations, are easy to find using a simple shortcut. This will be used for the rest of the method.
To calculate the slope of the tangent line, you need to take the first derivative, and add in the x value into your derivative to get your slope. For this method, consider the question: “What is the slope of the line f(x)=2x2+6x{\displaystyle f(x)=2x^{2}+6x} at the point (4,2)?"[12] X Research source The derivative is often written as f′(x),y′,{\displaystyle f’(x),y’,} or dydx{\displaystyle {\frac {dy}{dx}}}
Derivative: f′(x)=4x+6{\displaystyle f’(x)=4x+6}
What is the slope of the line f(x)=2x2+6x{\displaystyle f(x)=2x^{2}+6x} at the point (4,2)? Derivative of Equation: f′(x)=4x+6{\displaystyle f’(x)=4x+6} Plug in Point for x: f′(x)=4(4)+6{\displaystyle f’(x)=4(4)+6} Find the Slope: The slope of the f(x)=2x2+6x{\displaystyle f(x)=2x^{2}+6x} at (4,2) is 22.
f′(x)=4x+6{\displaystyle f’(x)=4x+6}
f′(x)=4(4)+6{\displaystyle f’(x)=4(4)+6}
Tangent lines are just lines with the exact same slope as your point on the curve. To draw one, go up (positive) or down (negative) your slope (in the case of the example, 22 points up). Then move over one and draw a point. Connect the dots, (4,2) and (26,3) for your line.
