Write the equation of a line (in slope-intercept form) through (5, 5) that is parallel to the line with endpoints (3,-2) an (7,-10).

Answer 1

Furst determine the slope of the line joining (3, -2) and (7, -10)

Use this slope in point-slope form.

Answer 2

The equation of a line in slope-intercept form follows the template y = mx + b, where m is the slope and b is the y-intercept. So, we need to find the slope and the y-intercept to write the equation of this line. First let's start with the slope; the hint here is the word "parallel" because parallel lines have the same slope. So, we need to calculate the slope of the line that runs through (3, -2) and (7, -10) by using the formula m = (y₂ - y₁)/(x₂ - x₁) = (-10 - -2)/(7 - 3) = (-10 + 2)/(7 - 3) = -8/4 = -2. The slope "m" of our new line must also be -2. Now onto the y-intercept "b": since we now have the slope -2, we can plug this AND the coordinate (5, 5) into the equation for x and y (respectively) to solve for b: y = mx + b --> y = -2x + b --> 5 = -2(5) + b. Use algebra to solve for b: 5 = -2(5) + b --> 5 = -10 + b --> 15 = b. Now that we solved for m (-2) and b (15), we can plug these values into the slope-intercept form to write the equation: y = -2x + 15