Find the equation of the line with gradient 2 and passing through (3, -1).

To determine the equation of a line with a gradient of 2 passing through the point (3, -1), we can use the point-slope form of a linear equation. The point-slope form is y – y1 = m(x – x1), where m represents the gradient and (x1, y1) is a point on the line. Substituting the values m = 2, x1 = 3, and y1 = -1 into the equation, we get y – (-1) = 2(x – 3). Simplifying this equation gives us y + 1 = 2x – 6.

Next, we can rewrite the equation in slope-intercept form, which is y = mx + b, where m is the gradient and b is the y-intercept. By rearranging the equation y + 1 = 2x – 6, we find y = 2x – 7. Therefore, the equation of the line with a gradient of 2 passing through the point (3, -1) is y = 2x – 7.

In conclusion, we have successfully found the equation of the line with a gradient of 2 passing through the point (3, -1) using the point-slope form and then converting it to the slope-intercept form. The equation y = 2x – 7 represents a line that has a slope of 2 and passes through the point (3, -1) on the Cartesian plane. This equation can be used to graph the line and determine its behaviour in relation to other lines or functions.

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