Final answer:
To write the equations in point-slope form and slope-intercept form, use the given information and follow the steps explained in the detailed answer. For the first equation, M = -2 and (3, -5) are given. The second equation is parallel to y = -4x + 2 and passes through (-1, 3).
Step-by-step explanation:
To write the equation of a line in point-slope form, we use the equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
a. Given that m = -2 and (3, -5) is a point on the line, the equation in point-slope form is y - (-5) = -2(x - 3). Simplifying this equation gives us y + 5 = -2x + 6.
Converting the equation to slope-intercept form, we isolate y. Subtracting 5 from both sides gives us y = -2x + 1 as the equation in slope-intercept form.
b. To find the equation of a line parallel to y = -4x + 2, we know that the slope of the parallel line will also be -4. Using the point (-1, 3), we can write the equation in point-slope form as y - 3 = -4(x - (-1)). Simplifying this equation gives us y - 3 = -4x - 4.
Converting the equation to slope-intercept form, we isolate y. Adding 3 to both sides gives us y = -4x - 1 as the equation in slope-intercept form.