Final answer:
The standard form of the linear equation is option B (-6x + y = 13), and the slope-intercept form is option C (y = -3/2x + 6). To find the graphs of the given equations, one must identify the slope and y-intercept for each equation.
Step-by-step explanation:
Determining Standard and Slope-Intercept Forms
Let's analyze the standard and slope-intercept forms of linear equations. The standard form of a linear equation is generally represented as Ax + By = C, where A, B, and C are integers, and A should be positive. The slope-intercept form is represented as y = mx + b, where m is the slope of the line, and b is the y-intercept.
To find the standard form from a set of options, one must ensure the x-term comes before the y-term, the leading coefficient (the number in front of x) is positive, and all terms are integers. From the provided options, the standard form that can be identified is B. -6x + y = 13, since it adheres to the principles of the standard form and is the only option where the coefficient of x is negative.
For the slope-intercept form of the equation, we look for an equation that is solved for y and written as y = mx + b. From the options given, the slope-intercept form is C. y = -3/2x + 6. This equation follows the structure of slope-intercept form, with -3/2 representing the slope and 6 representing the y-intercept.
To select the graph that represents the equation y = 1/3x - 5, we must identify a line that has a slope of 1/3 and a y-intercept of -5. Similarly, for the equation -4x - y = 2, we first need to rearrange it into slope-intercept form, yielding y = -4x - 2, and then choose a graph that displays a slope of -4 and a y-intercept of -2.