Unit 1: Analytic Geometry 3) Write the slope intercept form of the equation of the line through the given point with the given slope Then write the equation in standard form a) point (-1,-2) slope=-1 b) point (4,-5) slope=undefined c) points (4,5) and (1,-4) d) point (4,-3) parallel to y=(1)/(4)x-2

## Step 1: Finding the equation for (a)### Given the point and slope , we use the point-slope form: . Substituting the given values, we get , which simplifies to . Solving for , we get . To convert to standard form, we add to both sides, resulting in .## Step 2: Finding the equation for (b)### Given the point and an undefined slope, this indicates a vertical line. Vertical lines have the form , where is a constant. Since the line passes through , the equation is . This is already in standard form.## Step 3: Finding the equation for (c)### Given points and , we first find the slope using the formula . Substituting the given points, we get . Now, using the point-slope form with the point and slope , we have , which simplifies to . Solving for , we get . Converting to standard form, we subtract from both sides to get , or equivalently, .## Step 4: Finding the equation for (d)### Given the point and that the line is parallel to , the parallel line has the same slope. Thus, . Using the point-slope form with the point and slope , we have , which simplifies to . Solving for , we get . To convert to standard form, we multiply by 4 to get , and then subtract from both sides to get , or equivalently, .