Line c has an equation of y=−43x−3. Line d, which is parallel to line c, includes the point (−2,−2). What is the equation of line d?Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Q. Line c has an equation of y=−43x−3. Line d, which is parallel to line c, includes the point (−2,−2). What is the equation of line d?Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Find Slope of Line c: Determine the slope of line c. Line c has an equation of y=−43x−3. The slope of a line in the form y=mx+b is m, where m is the coefficient of x. The slope of line c is −43.
Determine Slope of Line d: Since line d is parallel to line c, it must have the same slope. The slope of line d is therefore also −43.
Use Point-Slope Form: Use the point-slope form to find the equation of line d. The point-slope form of a line is y−y1=m(x−x1), where m is the slope and (x1,y1) is a point on the line. We have the point (−2,−2) and the slope −43. Plugging these into the point-slope form gives us y−(−2)=−43(x−(−2)).
Convert to Slope-Intercept Form: Simplify the equation from the point-slope form to the slope-intercept form.y+2=−43(x+2)y+2=−43x−43(2)y+2=−43x−23Subtract 2 from both sides to get y by itself:y=−43x−23−2y=−43x−23−24y=−43x−27
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