Final answer:
Given the slope m = 9 and the point (3,5), the correct slope-intercept form of the line is y = 9x - 22, corresponding to option (a).
Step-by-step explanation:
The question pertains to finding the equation of a straight line in slope-intercept form, given a slope (m) and a point through which the line passes. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Since we are given the slope m = 9 and a point (3,5), we can substitute these values into the slope-intercept form to find the y-intercept (b).
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope is 9 and the point (3, 5) lies on the line. We can substitute these values into the equation to find the expression for the line.:
Substitute the slope value, m = 9, into the equation: y = 9x + b
Substitute the coordinates of the point, (3, 5), into the equation: 5 = 9(3) + b
Solve for b: b = 5 - 27 = -22
Therefore, the equation of the line in slope-intercept form is y = 9x - 22.
The process is as follows: plug in the point's x and y values, and the given slope into the slope-intercept equation, then solve for b:
- y = mx + b
- 5 = 9(3) + b
- 5 = 27 + b
- b = 5 - 27
- b = -22
Thus, the equation of the line is y = 9x - 22, which corresponds to option (a).