What is the Slope of y = 6x + 2 –
The slope of y = 6x + 2 is 6.
In the slope-intercept form of a linear equation, y = mx + b, the coefficient m directly gives the slope. Here, m = 6.
Understanding the Slope
The slope tells you how steep the line is and the direction it goes. A slope of 6 means that for every 1 unit you move right (positive x), the line rises 6 units up (positive y). It is a steep upward-sloping line.
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How to Find the Slope Step-by-Step
- Rewrite the equation in slope-intercept form (y = mx + b) if needed. The given equation y = 6x + 2 is already in this form.
- Identify the coefficient of x. That coefficient is the slope (m = 6).
- The constant term (+2) is the y-intercept (where the line crosses the y-axis).
You can also calculate slope using two points on the line with the formula: m = (y₂ – y₁) / (x₂ – x₁)
Example: When x = 0, y = 2 → Point (0, 2) When x = 1, y = 8 → Point (1, 8) Slope = (8 – 2) / (1 – 0) = 6 / 1 = 6
FAQs : What is the Slope of y = 6x + 2
What if the equation was y = 6x – 2?
The slope is still 6. Only the y-intercept changes (to -2).
How do you find the slope if the equation is not in y = mx + b form?
Rewrite it into slope-intercept form first. For example, from 2y – 12x = 4 → y = 6x + 2, slope = 6.
What does a slope of 6 look like?
It is a line that rises sharply. It makes an angle of about 80.5 degrees with the positive x-axis.
Is the slope always the coefficient of x?
Yes, when the equation is written in slope-intercept form (y = mx + b).