Final Answer:
The equation in slope-intercept form of the line that includes side CD is y = 1/2x + 4, which corresponds to option B.
Step-by-step explanation:
To find the equation of the line that includes side CD, we first need to determine the slope of side AB. The given line y = 1/4x - 3 is in slope-intercept form (y = mx + b), where m represents the slope. Comparing this equation with y = mx + b, we can see that the slope of side AB is 1/4. Since side CD is parallel to side AB, it will have the same slope.
Next, we use the point (-1,6) through which side CD passes to find the equation in slope-intercept form. Using the point-slope form of a linear equation (y - y1 = m(x - x1)), where (x1, y1) is the given point and m is the slope, we substitute the values to get the equation in slope-intercept form. After simplifying, we get y = 1/2x + 4, which matches option B.
Therefore, the equation in slope-intercept form of the line that includes side CD is y = 1/2x + 4.Final Answer:
The equation in slope-intercept form of the line that includes side CD is y = 1/2x + 4, which corresponds to option B.
Step-by-step explanation:
To find the equation of the line that includes side CD, we first need to determine the slope of side AB. The given line y = 1/4x - 3 is in slope-intercept form (y = mx + b), where m represents the slope. Comparing this equation with y = mx + b, we can see that the slope of side AB is 1/4. Since side CD is parallel to side AB, it will have the same slope.
Next, we use the point (-1,6) through which side CD passes to find the equation in slope-intercept form. Using the point-slope form of a linear equation (y - y1 = m(x - x1)), where (x1, y1) is the given point and m is the slope, we substitute the values to get the equation in slope-intercept form. After simplifying, we get y = 1/2x + 4, which matches option B.
Therefore, the equation in slope-intercept form of the line that includes side CD is y = 1/2x + 4.