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A line has a slope of 55 and includes the points (−5,2)(-5,2) and (−6,r)(-6,r). What is the value of rr?\newliner = ____

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Full solution

Q. A line has a slope of 55 and includes the points (−5,2)(-5,2) and (−6,r)(-6,r). What is the value of rr?\newliner = ____
  1. Understand slope concept: Understand the concept of slope. The slope of a line is the ratio of the change in the yy-coordinate to the change in the xx-coordinate between any two points on the line. It is often represented as mm in the slope formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.
  2. Apply slope formula: Apply the slope formula to the given points and slope.\newlineWe know the slope mm is 55, one point is (−5,2)(-5,2), and the other point is (−6,r)(-6,r). We can plug these values into the slope formula:\newline5=r−2−6−(−5)5 = \frac{r - 2}{-6 - (-5)}
  3. Simplify denominator: Simplify the denominator of the fraction.\newline−6−(−5)-6 - (-5) simplifies to −6+5-6 + 5, which equals −1-1.\newlineSo, the equation becomes:\newline5=r−2−15 = \frac{r - 2}{-1}
  4. Solve for r: Solve for r.\newlineTo find r, we multiply both sides of the equation by −1-1:\newline5×−1=(r−2)5 \times -1 = (r - 2)\newline−5=r−2-5 = r - 2
  5. Isolate rr: Isolate rr by adding 22 to both sides of the equation.\newline−5+2=r-5 + 2 = r\newliner=−3r = -3

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