The equation -4x - y = -3 can be rewritten in slope-intercept form as y = -4x + 3, which indicates a slope of -4 and a y-intercept of 3. Hence, the graph is a line with a slope of -4 and intersects the y-axis at 3.
To find the slope-intercept form of the given equation, -4x - y = -3, we need to solve for y in terms of x. We start by adding 4x to both sides of the equation to get -y = 4x - 3. Then, we multiply both sides by -1 to isolate y, resulting in y = -4x + 3. This is the slope-intercept form, where the coefficient of x represents the slope and the constant term represents the y-intercept.
According to this form, the slope is -4 and the y-intercept is 3. In graphing this equation, one can start at the y-intercept (0, 3) and, because the slope is -4, move down four units vertically for every one unit moved to the right horizontally to plot a second point, thereby determining the line's direction and steepness.
Therefore, the correct option that matches the slope-intercept form of the given equation and the graph description is: a) Slope-intercept form: y = -4x + 3, Graph: A line with slope -4 and y-intercept at 3.