Shamya needs to find 2 points to help her graph a line.She knows that the line goes through the point (2,1) and has a slope of -(5)/(3) -5 -5 -4 -8 -1 -2 -3 -6

To find another point on the line, we can use the point-slope form of a linear equation, which is given by:<br /><br />\[ y - y_1 = m(x - x_1) \]<br /><br />where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. In this case, the point \( (2, 1) \) is on the line, and the slope \( m \) is \(-\frac{5}{3}\).<br /><br />Let's find another point by choosing a different \( x \)-value. We can choose an \( x \)-value that makes calculations simple. Let's choose \( x = 5 \).<br /><br />Substitute \( x = 5 \) into the point-slope formula:<br /><br />\[ y - 1 = -\frac{5}{3}(5 - 2) \]<br /><br />Calculate the right side:<br /><br />\[ y - 1 = -\frac{5}{3} \times 3 \]<br /><br />\[ y - 1 = -5 \]<br /><br />Add 1 to both sides to solve for \( y \):<br /><br />\[ y = -5 + 1 \]<br /><br />\[ y = -4 \]<br /><br />So, another point on the line is \( (5, -4) \).<br /><br />Therefore, the two points Shamya can use to graph the line are \( (2, 1) \) and \( (5, -4) \).