Final answer:
The equation of a line parallel to −2y=4−2x that passes through (-5,9) is written in slope-intercept form as y = x + 14.
Step-by-step explanation:
To find the equation of a line parallel to −2y=4−2x that passes through the point (-5,9), we first need to rewrite the given equation in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. Starting with −2y = 4 − 2x, divide both sides by −2 to get y = −2x − 2. Now, since the slope of the parallel line must be the same as the slope of the given line, the slope (m) is 1. This means our new equation will have the same slope, which is y = 1x + b.
To find the y-intercept (b), we substitute the x and y values from the given point through which the new line will pass: 9 = 1(−5) + b. Solving for b gives us b = 9 + 5, so b = 14. Therefore, the equation of the line that is parallel to the given line and passes through (-5,9) is y = x + 14.