If f′(−2) = 7, find an equation of the line tangent to the graph of f at the point (−2,4).

Verified step by step guidance

1. Step 1: Recall that the equation of a line in point-slope form is given by y - y_1 = m(x - x_1), where m is the slope and (x_1, y_1) is a point on the line.
2. Step 2: Identify the slope of the tangent line. Since f'(-2) = 7, the slope of the tangent line at x = -2 is 7.
3. Step 3: Identify the point on the graph where the tangent line touches. The problem states that the point is (-2, 4).
4. Step 4: Substitute the slope (m = 7) and the point (-2, 4) into the point-slope form equation: y - 4 = 7(x + 2).
5. Step 5: Simplify the equation if needed to express it in a different form, such as slope-intercept form (y = mx + b), by distributing and rearranging terms.