Final answer:
The equation y = m(x - h) + k can indeed be graphed directly without converting to slope-intercept form as it provides sufficient information, specifically the slope and a point on the line, to plot the graph accurately, making it true.The correct option is a) True
Step-by-step explanation:
The equation y = m(x - h) + k is known as the point-slope form of the equation of a straight line, where m represents the slope of the line, and (h, k) are the coordinates of a point on the line. The question asks about graphing this equation directly without converting it to the slope-intercept form, which is typically y = mx + b, where m is the slope and b is the y-intercept.
To graph the point-slope form directly, one can plot the point (h, k) on the graph which gives the exact location of the line on the coordinate plane. From this point, you use the slope m (rise over run) to find other points on the line. Since you are using the actual point and the slope, there is no need to convert to slope-intercept form first thus making the statement True.
It's important to remember the relation between these two forms and how the components of each form determine where the line is situated on the graph. The slope m indicates how steep the line is, and the point (h, k) allows us to find the exact line that has that slope and passes through that point.The correct option is a) True