Final answer:
The line with slope 4 passing through the point (-2, 7) is represented by the equation y = 4x + 15. Therefore, the correct answer is option (a).
Step-by-step explanation:
To graph a line that contains the point (-2, 7) and has a slope of 4, we can use the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Since we are given a slope of 4, our equation will have the form y = 4x + b. To find the y-intercept (b), we can substitute the coordinates of the given point (-2, 7) into the equation, which gives us 7 = 4(-2) + b.
Solving for b, we get: 7 = -8 + b which simplifies to b = 15.
Therefore, the equation of the line is y = 4x + 15. Out of the given options, (a) y = 4x + 15 is the correct equation for the line that passes through the point (-2, 7) with a slope of 4. The mention correct option answer in the final answer is option (a).